Method and device for calculating stresses of downhole tools in curved well sections

Abstract

The application discloses a calculation method and device for stress of a downhole tool in a curved well section, and the calculation method comprises the following steps: judging whether the bending of the downhole tool is conventional bending or limit bending based on actual working conditions of the downhole tool; if the bending of the downhole tool is conventional bending, a first displacement function of the downhole tool in the conventional bending is constructed; the first displacement function is loaded into finite element software for analysis; if the bending of the downhole tool is limit bending, a second displacement function of the downhole tool in the limit bending is constructed, and the second displacement function is loaded into the finite element software for analysis. According to the calculation method for the stress of the downhole tool in the curved well section, the actual bending working condition of the actual downhole tool can be well simulated, and then the stress value can be solved.

Description

Technical Field

[0001] This invention relates to a method for calculating the stress of downhole tools passing through curved well sections, specifically to a method, apparatus, computing device, and computer storage medium for calculating the stress of downhole tools passing through curved well sections. Background Technology

[0002] The oil development process involves multiple stages, including oil exploration, drilling, logging, well logging, cementing, and well completion, before a channel can be built to bring the target oil layer to the surface.

[0003] Oil wells typically follow a curved path beyond a certain depth, with some sections exhibiting significant curvature. As downhole tools traverse these curved sections, they are subjected to forced bending from the wellbore. This is particularly pronounced when the curvature of the well section is substantial and the outer diameter of the downhole tool is close to the wellbore diameter, resulting in significant bending of the tool.

[0004] The impact of this working condition on the strength of downhole tools should be considered during the design process. Therefore, the maximum stress of the downhole tool needs to be calculated under this condition. Downhole tools typically have complex structures, requiring the use of finite element method (FEM) software for strength calculations. The setting of the FEM boundary conditions significantly affects the accuracy of the stress calculation results for downhole tools. Therefore, the FEM boundary conditions should be as consistent as possible with the downhole bending condition while also satisfying geometric conditions and software settings. In existing technologies, most designs are based on analogy, and many downhole tools do not undergo strength calculations under bending conditions, failing to accurately simulate the actual bending characteristics of real downhole tools. Summary of the Invention

[0005] In view of the above problems, the present invention is proposed to provide a method, apparatus, computing device, and computer storage medium for calculating the stress of downhole tools in curved well sections that overcomes or at least partially solves the above problems.

[0006] According to one aspect of the present invention, a method for calculating the stress of downhole tools passing through curved well sections is provided, comprising:

[0007] Based on the actual working conditions of the downhole tool, determine whether the bending of the downhole tool is normal bending or extreme bending;

[0008] If the bending of the downhole tool is a conventional bending, then construct the first displacement function of the downhole tool with conventional bending;

[0009] Analysis was performed by loading the first displacement function using finite element software.

[0010] If the bending of the downhole tool is a limiting bending, then construct the second displacement function of the downhole tool for limiting bending; and

[0011] The analysis was performed by loading a second displacement function using finite element software.

[0012] Optionally, constructing a first displacement function for a conventionally curved downhole tool further includes:

[0013] The first displacement function of a downhole tool under conventional bending is constructed based on a computational model of a simply supported beam subjected to concentrated forces; and

[0014] Constructing a second displacement function for a downhole tool with extreme bending further includes:

[0015] The second displacement function of the downhole tool under extreme bending is constructed based on the constant curvature circle model.

[0016] The first displacement function of a conventionally bent downhole tool is constructed based on a calculation model of a simply supported beam subjected to concentrated forces, and further includes:

[0017] The maximum deflection of a conventionally curved downhole tool is calculated based on the geometric relationship between the conventionally curved downhole tool and the curved well section.

[0018] Calculation of concentrated forces on a simply supported beam under concentrated force based on a computational model; and

[0019] Based on the concentrated force borne by a conventionally curved downhole tool, the deflection equation of the conventionally curved downhole tool is determined, and the displacement function of any point on the conventionally curved downhole tool is obtained.

[0020] The analysis was performed by loading the first displacement function using finite element software, and further included:

[0021] Set the first boundary conditions for conventionally curved downhole tools;

[0022] Finite element mesh generation was performed on a conventionally curved downhole tool using finite element software.

[0023] Obtain the stresses experienced by a conventionally bent downhole tool corresponding to each finite element mesh; and

[0024] To obtain the maximum stress that a conventionally bent downhole tool can withstand.

[0025] Setting the first boundary conditions for conventional curved downhole tools further includes:

[0026] A first displacement function is applied along the longitudinal axis of a conventionally curved downhole tool;

[0027] The degrees of freedom in the horizontal and vertical directions of a conventionally curved downhole tool are set to 0.

[0028] The contact between the conventionally curved downhole tool and the side of the first connector closest to the conventionally curved downhole tool is a bonded contact; the contact between the conventionally curved downhole tool and the middle portion of the first connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the first connector furthest from the conventionally curved downhole tool is a non-separating contact; and

[0029] The contact between the conventionally curved downhole tool and the side of the second connector closest to the conventionally curved downhole tool is a binding contact; the contact between the conventionally curved downhole tool and the middle part of the second connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the second connector furthest from the conventionally curved downhole tool is a non-separating contact.

[0030] Optionally, the analysis is performed by loading a second displacement function using finite element software, further including:

[0031] Set the second boundary condition for the downhole tool to limit bending;

[0032] Finite element mesh generation was performed on the downhole tool under extreme bending using finite element software.

[0033] Obtain the stresses experienced by the downhole tool under extreme bending, corresponding to each finite element mesh; and

[0034] The maximum stress that a downhole tool can withstand when it reaches its limit of bending.

[0035] Optionally, a second boundary condition is set for the downhole tool to limit bending, further including:

[0036] A second displacement function is applied along the longitudinal axis of the downhole tool under extreme bending.

[0037] The degrees of freedom in the horizontal and vertical directions of the downhole tool under extreme bending are set to 0;

[0038] The contact between the downhole tool with its extreme bending limit and the side of the first connector closest to the extreme bending limit is a bonded contact; the contact between the downhole tool with its extreme bending limit and the middle portion of the first connector is a non-separating contact; the contact between the downhole tool with its extreme bending limit and the end face of the first connector furthest from the extreme bending limit is a non-separating contact; and

[0039] The contact between the downhole tool with extreme bending and the side of the second connector closest to the downhole tool with extreme bending is a bonded contact; the contact between the downhole tool with extreme bending and the middle part of the second connector is a non-separating contact; the contact between the downhole tool with extreme bending and the end face of the second connector away from the downhole tool with extreme bending is a non-separating contact.

[0040] According to another aspect of the present invention, a calculation apparatus for the stress of a downhole tool passing through a curved well section is provided, the calculation apparatus comprising:

[0041] The judgment module is suitable for determining whether the bending of the downhole tool is normal bending or extreme bending based on the actual working conditions of the downhole tool.

[0042] The first building block is suitable for building the first displacement function of a conventionally curved downhole tool;

[0043] The first analysis module is suitable for analysis by loading the first displacement function using finite element software;

[0044] A second building block, suitable for constructing a second displacement function for downhole tools subject to extreme bending; and

[0045] The second analysis module is suitable for analysis by loading a second displacement function using finite element software.

[0046] Optionally, the first building module is further adapted to:

[0047] The first displacement function of a downhole tool under conventional bending is constructed based on a computational model of a simply supported beam subjected to concentrated forces; and

[0048] The second building module is further adapted to:

[0049] The second displacement function of the downhole tool under extreme bending is constructed based on the constant curvature circle model.

[0050] Optionally, the first building module is further adapted to:

[0051] The maximum deflection of a conventionally curved downhole tool is calculated based on the geometric relationship between the conventionally curved downhole tool and the curved well section.

[0052] Calculation of concentrated forces on a simply supported beam under concentrated force based on a computational model; and

[0053] Based on the concentrated force borne by a conventionally curved downhole tool, the deflection equation of the conventionally curved downhole tool is determined, and the displacement function of any point on the conventionally curved downhole tool is obtained.

[0054] Optionally, the first analysis module is further adapted to:

[0055] Set the first boundary conditions for conventionally curved downhole tools;

[0056] Finite element mesh generation was performed on a conventionally curved downhole tool using finite element software.

[0057] Obtain the stresses experienced by a conventionally bent downhole tool corresponding to each finite element mesh; and

[0058] To obtain the maximum stress that a conventionally bent downhole tool can withstand.

[0059] Optionally, the first analysis module is further adapted to:

[0060] A first displacement function is applied along the longitudinal axis of a conventionally curved downhole tool;

[0061] The degrees of freedom in the horizontal and vertical directions of a conventionally curved downhole tool are set to 0.

[0062] The contact between the conventionally curved downhole tool and the side of the first connector closest to the conventionally curved downhole tool is a bonded contact; the contact between the conventionally curved downhole tool and the middle portion of the first connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the first connector furthest from the conventionally curved downhole tool is a non-separating contact; and

[0063] The contact between the conventionally curved downhole tool and the side of the second connector closest to the conventionally curved downhole tool is a binding contact; the contact between the conventionally curved downhole tool and the middle part of the second connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the second connector furthest from the conventionally curved downhole tool is a non-separating contact.

[0064] Optionally, the second analysis module is further adapted to:

[0065] Set the second boundary condition for the downhole tool to limit bending;

[0066] Finite element mesh generation was performed on the downhole tool under extreme bending using finite element software.

[0067] Obtain the stresses experienced by the downhole tool under extreme bending, corresponding to each finite element mesh; and

[0068] The maximum stress that a downhole tool can withstand when it reaches its limit of bending.

[0069] Optionally, the second analysis module is further adapted to:

[0070] A second displacement function is applied along the longitudinal axis of the downhole tool under extreme bending.

[0071] The degrees of freedom in the horizontal and vertical directions of the downhole tool under extreme bending are set to 0;

[0072] The contact between the downhole tool with its extreme bending limit and the side of the first connector closest to the extreme bending limit is a bonded contact; the contact between the downhole tool with its extreme bending limit and the middle portion of the first connector is a non-separating contact; the contact between the downhole tool with its extreme bending limit and the end face of the first connector furthest from the extreme bending limit is a non-separating contact; and

[0073] The contact between the downhole tool with extreme bending and the side of the second connector closest to the downhole tool with extreme bending is a bonded contact; the contact between the downhole tool with extreme bending and the middle part of the second connector is a non-separating contact; the contact between the downhole tool with extreme bending and the end face of the second connector away from the downhole tool with extreme bending is a non-separating contact.

[0074] According to another aspect of the present invention, a computing device is provided, comprising: a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other via the communication bus;

[0075] The memory is used to store at least one executable instruction that causes the processor to perform the operation corresponding to the above-described method for calculating the stress of downhole tools passing through curved well sections.

[0076] According to another aspect of the present invention, a computer storage medium is provided, wherein at least one executable instruction is stored therein, the executable instruction causing a processor to perform an operation corresponding to the above-described method for calculating the stress of a downhole tool passing through a curved well section.

[0077] According to the present invention, a method, apparatus, computing device, and computer storage medium for calculating the stress of downhole tools passing through curved well sections determine whether the bending of the downhole tool is conventional or extreme based on the actual working conditions of the downhole tool. If the bending is conventional, a first displacement function for the conventionally bent downhole tool is constructed and analyzed using finite element software. If the bending is extreme, a second displacement function for the extreme bending downhole tool is constructed and analyzed using finite element software. Based on the stress calculation method of downhole tools passing through curved well sections according to this scheme, by deriving the displacement function and setting boundary conditions and loading the displacement function in the finite element software, the actual bending conditions of the downhole tool can be well simulated to solve for the stress value.

[0078] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0079] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0080] Figure 1This diagram illustrates a downhole tool in a conventionally curved state when navigating a curved well section.

[0081] Figure 2a and Figure 2b This diagram illustrates the downhole tool under extreme bending conditions when navigating a curved well section.

[0082] Figure 3 A flowchart illustrating a method for calculating the stress of a downhole tool passing through a curved well section according to Embodiment 1 of the present invention is shown.

[0083] Figure 4 A schematic diagram illustrating the geometric relationship between a conventional curved downhole tool and a curved well section according to Embodiment 1 of the present invention is shown.

[0084] Figure 5 A geometrical schematic diagram is shown below, illustrating the calculation of the concentrated force borne by a conventionally bent downhole tool using a calculation model based on a simply supported beam subjected to concentrated force according to Embodiment 1 of the present invention.

[0085] Figure 6 A schematic diagram of the boundary conditions for a conventional curved downhole tool according to Embodiment 1 of the present invention is shown;

[0086] Figure 7 A partial screenshot of the meshing of a conventional curved downhole tool according to Embodiment 1 of the present invention is shown;

[0087] Figure 8 A schematic diagram of the stress results of a conventionally curved downhole tool obtained by the stress calculation method of a downhole tool in a curved well section according to Embodiment 1 of the present invention is shown.

[0088] Figure 9 A schematic diagram illustrating the geometric relationship between a downhole tool subject to extreme bending and a bent well section according to Embodiment 1 of the present invention is shown.

[0089] Figure 10 A geometrical schematic diagram is shown, illustrating the calculation of the concentrated force borne by a downhole tool under extreme bending according to a computational model based on a circle of constant curvature according to Embodiment 1 of the present invention.

[0090] Figure 11 A schematic diagram of the stress results of a downhole tool under extreme bending, obtained by the method for calculating the stress of a downhole tool in a bent well section according to Embodiment 1 of the present invention, is shown.

[0091] Figure 12 A schematic diagram of the apparatus for calculating the stress of downhole tools passing through curved well sections according to Embodiment 2 of the present invention is shown; and

[0092] Figure 13 A schematic diagram of the structure of a computing device provided according to Embodiment 3 of the present invention is shown. Detailed Implementation

[0093] Exemplary embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this invention will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0094] In the field of oil development, wellbore curvature is a parameter referring to the degree of bending of the wellbore axis. The wellbore trajectory is a continuous, smooth spatial curve formed during actual drilling. The angle between the two tangent vectors at the start and end points of the wellbore trajectory in the direction of travel is defined as the bending angle. These two tangent vectors are usually not located in the same plane, therefore the bending angle is a spatial angle. This spatial angle is figuratively called the "dogleg angle" or "full angle." There are two methods to represent wellbore curvature: the rate of change of the full angle and the dogleg severity. The rate of change of the full angle is defined as "the change in the angle of the wellbore axis per unit well length in three-dimensional space." It includes both the change in the inclination angle and the change in the azimuth angle. In domestic drilling, it is generally expressed in ° / 30m, that is, the change in the angle between the tangents at the start and end points every 30 meters.

[0095] The wellbore trajectory is a spatial arc caused by changes in both inclination and azimuth. In this invention, to simplify calculations, it is assumed that within a 30-meter wellbore trajectory, only one angle of inclination or azimuth changes, and the wellbore trajectory at this time is a planar arc. It is also assumed that the change in the wellbore trajectory is uniform.

[0096] When a downhole tool passes through a curved section of the well, both ends of the downhole tool are restricted by the upper well wall, and the middle part of the downhole tool is restricted by the lower well wall. This type of curvature is called conventional curvature.

[0097] When downhole tools encounter resistance during descent or jamming during descent when navigating curved sections of the well, applying a large axial force to the tool can cause it to bend against the casing wall; this bending is called ultimate bending.

[0098] Figure 1 The diagram illustrates a downhole tool in a conventionally curved position when traversing a curved well section. In this invention, the downhole tool is, for example, a perforating gun, but the specific type is not limited. Figure 1 As shown, when a downhole tool passes through a curved section of the well, both ends of the downhole tool are restricted by the upper well wall, and the middle part of the downhole tool is restricted by the lower well wall. Therefore, when the downhole tool passes through a section of the well that is curved to a certain extent, it will inevitably be forced to bend.

[0099] Figure 2a and Figure 2bThis diagram illustrates the downhole tool at its limit of bending when navigating a curved well section. Figure 2a This illustrates the situation where a downhole tool is forced to bend and presses against the lower wellbore wall as it passes through a curved section of the well. Figure 2b This illustrates the situation where a downhole tool is forced to bend and press against the upper well wall when passing through a curved section of the well.

[0100] The following specific embodiments will illustrate the method for calculating the stress of downhole tools passing through curved well sections according to the present invention.

[0101] Example 1

[0102] Figure 3 A flowchart illustrating a method for calculating the stress of downhole tools traversing a curved well section according to Embodiment 1 of the present invention is shown. Figure 3 As shown, the method includes:

[0103] Step S110: Based on the actual working conditions of the downhole tool, determine whether the bending of the downhole tool is normal bending or extreme bending.

[0104] Specifically, if the downhole tool is restricted at both ends by the upper well wall and in the middle by the lower well wall when passing through a curved section, the bending of the downhole tool is judged as a normal bending. If the downhole tool encounters resistance when lowering or gets stuck when lifting, and applying a large axial force to the downhole tool will cause it to bend against the casing wall, the bending of the downhole tool is judged as extreme bending.

[0105] Step S121: If the bending of the downhole tool is a conventional bending, then construct the first displacement function of the conventionally bent downhole tool.

[0106] Based on the judgment in step S110, when the bending of the downhole tool is conventional bending, the first displacement function of the downhole tool under conventional bending is constructed based on the calculation model of a simply supported beam under concentrated force.

[0107] Specifically, the maximum deflection of the conventionally curved downhole tool is calculated based on the geometric relationship between the conventionally curved downhole tool and the curved well section; the concentrated force borne by the conventionally curved downhole tool is calculated based on the calculation model of a simply supported beam subjected to concentrated force; and based on the concentrated force borne by the conventionally curved downhole tool, the deflection equation of the conventionally curved downhole tool is determined, and the displacement function of any point of the conventionally curved downhole tool is obtained.

[0108] Specifically, Figure 4A schematic diagram of the geometric relationship of a downhole tool passing through a conventional curved well section according to Embodiment 1 of the present invention is shown. In this embodiment, the wellbore trajectory is a planar circular arc, and it is assumed that the change in the wellbore trajectory is uniform. The diameter of the downhole tool is 127 mm, and the diameter of the curved well section is 152.4 mm. Based on the geometric relationship between the conventional curved downhole tool and the curved well section, the following formulas (1)-(3) can be obtained:

[0109]

[0110]

[0111] ω 1max =ω0-(152.4-127) (3)

[0112] Where L is the length of the downhole tool, set at 9m, and the total angle variation rate is 8° / 30m, ψ0 can be calculated to be 47.1mm. 1max It is 21.7mm.

[0113] Figure 5 A geometrical schematic diagram is shown below, illustrating the calculation model based on a simply supported beam subjected to concentrated force according to Embodiment 1 of the present invention, for calculating the concentrated force borne by a conventionally bent downhole tool. Combining the deflection curve equation of a simply supported beam subjected to concentrated force in mechanics of materials and the above formulas (1)-(3), formula (4) can be obtained:

[0114]

[0115] By transforming formula (4), we can obtain formula (5):

[0116]

[0117] Where EI is the cross-sectional parameter, and with the cross-sectional dimensions of the downhole tool being 127mm×11mm, the length of the downhole tool being 9m, and the concentrated force F acting on the middle position of the downhole tool, we can obtain F=1943.1N.

[0118] According to the law of materials mechanics, when a concentrated force F is applied to the midpoint of a simply supported beam, its deflection ω can be expressed as formula (6):

[0119]

[0120] Substituting the cross-sectional parameters EI, L, and F, we can obtain the first displacement function of ω1 (the deflection value at any point on the beam, i.e., the deflection value at any point of a conventionally bent downhole tool) with respect to x, namely, formula (7):

[0121] ω1=29.765x×10 -6 (243-4x 2(7)

[0122] Step S131: Load the first displacement function using finite element software for analysis.

[0123] Specifically, the analysis is performed by loading the first displacement function (i.e., Equation (7)) using finite element software, including: setting the first boundary conditions for the conventionally curved downhole tool; performing finite element mesh generation on the conventionally curved downhole tool using finite element software; obtaining the stress borne by the conventionally curved downhole tool corresponding to each finite element mesh; and obtaining the maximum stress borne by the conventionally curved downhole tool.

[0124] Figure 6 A schematic diagram of the boundary conditions for a conventionally curved downhole tool according to Embodiment 1 of the present invention is shown. Specifically, the first boundary condition for the conventionally curved downhole tool is set as follows: 1) A first displacement function is applied in the longitudinal direction of the conventionally curved downhole tool, wherein the longitudinal direction is specifically... Figure 6 In the Y-axis direction, and in Figure 6 1) Apply the first displacement function at boundary 1; 2) Set the degrees of freedom of the horizontal and vertical axes of the conventional curved downhole tool to 0, specifically the horizontal axis as follows: Figure 6 The X-axis direction and the vertical axis direction are... Figure 6 The Z-axis direction (perpendicular to the paper and outwards, not shown) in Figure 6 Boundaries 2 and 3 restrict the horizontal and vertical movement of the conventionally curved downhole tool, i.e., the degree of freedom is 0; 3) The conventionally curved downhole tool contacts the side of the first joint A closest to the conventionally curved downhole tool. Figure 6 The four boundary points are the binding contact points, and the contact between the conventionally curved downhole tool and the middle part of the first joint A is the binding contact point. Figure 6 At the boundary 5 points, there is no separation contact; the contact between the conventionally curved downhole tool and the end face of the first joint A on the side away from the conventionally curved downhole tool ( Figure 6 (6 points at the boundary) are in non-separation contact; 4) the conventionally bent downhole tool and the second joint B ( Figure 6 The contact between the right overlapping portion of the first connector A and the side of the conventionally curved downhole tool closest to it is a binding contact; the contact between the conventionally curved downhole tool and the middle portion of the second connector B is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the second connector B on the side furthest from the conventionally curved downhole tool is a non-separating contact. Specifically, the first connector A and the second connector B can be the same.

[0125] Figure 7A partial screenshot of the mesh generation for a conventionally curved downhole tool according to Embodiment 1 of the present invention is shown. The conventionally curved downhole tool was meshed using finite element software. The overall mesh type was tetrahedral, the downhole tool mesh size was set to 5 mm, the joint mesh size was set to 20 mm, and the transition type was slow. All contact areas had a mesh size of 2 mm. The total number of meshes was approximately 800,000, with approximately 1.27 million nodes. Based on the mesh generation, the stresses experienced by the conventionally curved downhole tool corresponding to each finite element mesh were obtained. Figure 8 The diagram illustrates the stress results of a conventionally curved downhole tool obtained by the stress calculation method for downhole tools in curved well sections according to Embodiment 1 of the present invention. Figure 8 As shown, the maximum stress occurs at the maximum outer diameter of the conventionally bent downhole tool, with a maximum value of 85.8 MPa.

[0126] Step S122: If the bending of the downhole tool is a limit bending, then construct the second displacement function of the downhole tool with limit bending.

[0127] Figure 9 A schematic diagram illustrating the geometric relationship between a downhole tool subject to extreme bending and a bent well section according to Embodiment 1 of the present invention is shown, as follows: Figure 9 As shown, the downhole tool is closely attached to the upper wall of the curved wellbore, ω 2max =ω0, ω can be calculated based on formulas (1)-(2) in step S121. 2max =47.1.

[0128] Figure 10 A geometrical schematic diagram is shown illustrating the calculation of the concentrated force borne by a downhole tool under limiting bending using a computational model based on a circle of constant curvature according to Embodiment 1 of the present invention. Figure 10 As shown, when the downhole tool is under extreme bending, it is in close contact with the wellbore. In this embodiment, it is assumed that the bending section is a planar circular arc, so the bending curve of the downhole tool is a circle of constant curvature. Using the geometric relationship formula, the function of ω2 with respect to x can be obtained, i.e., formula (8):

[0129]

[0130] Combine L value and ω 2max Substituting into equation (8), we can obtain the second displacement function of ω2 (the deflection value at any point of the downhole tool under ultimate bending) with respect to x, namely, equation (9):

[0131]

[0132] Step S132: Analyze the second displacement function using finite element software.

[0133] Specifically, the analysis is performed by loading the second displacement function (i.e., Equation (9)) using finite element software, including: setting the second boundary conditions of the downhole tool with extreme bending; performing finite element mesh generation on the downhole tool with extreme bending using finite element software; obtaining the stress borne by the downhole tool with extreme bending corresponding to each finite element mesh; and obtaining the maximum stress borne by the downhole tool with extreme bending.

[0134] Specifically, the second boundary condition for the extreme bending downhole tool is set as follows: the second displacement function obtained in step S122 is applied along the longitudinal axis of the extreme bending downhole tool. The application direction and position of the second displacement function are consistent with the application direction and position of the first displacement function in step S131, and will not be repeated here. The boundary conditions in the other directions of the extreme bending downhole tool are also consistent with the setting of the first boundary condition in step S131, and will not be repeated here.

[0135] The mesh generation for the downhole tool under extreme bending is consistent with that for the conventional bending downhole tool in step S131, and will not be repeated here. Based on the maximum stress results of the conventional bending downhole tool, the stress calculation for the downhole tool under extreme bending directly uses a model with a hole density of 60 holes / m, a single support length of 2.2 meters, and a central joint combination. Figure 11 A schematic diagram showing the stress results of a downhole tool under extreme bending, obtained by the method for calculating the stress of a downhole tool in a bent well section according to Embodiment 1 of the present invention, is illustrated. Figure 11 As shown, the maximum stress occurs at the maximum outer diameter of the barrel, with a maximum value of 154 MPa.

[0136] According to the stress calculation method of downhole tools passing through curved well sections in this embodiment, by deriving the displacement function, setting boundary conditions and loading the displacement function in the finite element software, the actual bending condition of the downhole tool can be well simulated and the stress value can be solved.

[0137] Example 2

[0138] Figure 12 A functional structural diagram of a downhole tool stress calculation device 200 for a curved well section, according to Embodiment 2 of the present invention, is shown. Figure 12 As shown, the computing device 200 includes: a judgment module 210, a first construction module 221, a first analysis module 231, a second construction module 222, and a second analysis module 232.

[0139] The judgment module 210 is suitable for determining whether the bending of the downhole tool is a normal bending or an extreme bending based on the actual working conditions of the downhole tool.

[0140] The first building module 221 is adapted to build the first displacement function of a conventionally curved downhole tool;

[0141] The first analysis module 231 is suitable for performing analysis by loading a first displacement function using finite element software;

[0142] The second building module 222 is adapted to build a second displacement function for a downhole tool with extreme bending; and

[0143] The second analysis module 232 is suitable for analysis by loading a second displacement function using finite element software.

[0144] In an alternative implementation, the first building module 221 is further adapted to:

[0145] The first displacement function of a downhole tool under conventional bending is constructed based on a computational model of a simply supported beam subjected to concentrated forces; and

[0146] The second building module 222 is further adapted to:

[0147] The second displacement function of the downhole tool under extreme bending is constructed based on the constant curvature circle model.

[0148] In an alternative implementation, the first building module 221 is further adapted to:

[0149] The maximum deflection of a conventionally curved downhole tool is calculated based on the geometric relationship between the conventionally curved downhole tool and the curved well section.

[0150] Calculation of concentrated forces on a simply supported beam under concentrated force based on a computational model; and

[0151] Based on the concentrated force borne by a conventionally curved downhole tool, the deflection equation of the conventionally curved downhole tool is determined, and the displacement function of any point on the conventionally curved downhole tool is obtained.

[0152] In an alternative implementation, the first analysis module 231 is further adapted to:

[0153] Set the first boundary conditions for conventionally curved downhole tools;

[0154] Finite element mesh generation was performed on a conventionally curved downhole tool using finite element software.

[0155] Obtain the stresses experienced by a conventionally bent downhole tool corresponding to each finite element mesh; and

[0156] To obtain the maximum stress that a conventionally bent downhole tool can withstand.

[0157] In an alternative implementation, the first analysis module 231 is further adapted to:

[0158] A first displacement function is applied along the longitudinal axis of a conventionally curved downhole tool;

[0159] The degrees of freedom in the horizontal and vertical directions of a conventionally curved downhole tool are set to 0.

[0160] The contact between the conventionally curved downhole tool and the side of the first connector closest to the conventionally curved downhole tool is a bonded contact; the contact between the conventionally curved downhole tool and the middle portion of the first connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the first connector furthest from the conventionally curved downhole tool is a non-separating contact; and

[0161] The contact between the conventionally curved downhole tool and the side of the second connector closest to the conventionally curved downhole tool is a binding contact; the contact between the conventionally curved downhole tool and the middle part of the second connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the second connector furthest from the conventionally curved downhole tool is a non-separating contact.

[0162] In an alternative implementation, the second analysis module 232 is further adapted to:

[0163] Set the second boundary condition for the downhole tool to limit bending;

[0164] Finite element mesh generation was performed on the downhole tool under extreme bending using finite element software.

[0165] Obtain the stresses experienced by the downhole tool under extreme bending, corresponding to each finite element mesh; and

[0166] The maximum stress that a downhole tool can withstand when it reaches its limit of bending.

[0167] In an alternative implementation, the second analysis module 232 is further adapted to:

[0168] A second displacement function is applied along the longitudinal axis of the downhole tool under extreme bending.

[0169] The degrees of freedom in the horizontal and vertical directions of the downhole tool under extreme bending are set to 0;

[0170] The contact between the downhole tool with its extreme bending limit and the side of the first connector closest to the extreme bending limit is a bonded contact; the contact between the downhole tool with its extreme bending limit and the middle portion of the first connector is a non-separating contact; the contact between the downhole tool with its extreme bending limit and the end face of the first connector furthest from the extreme bending limit is a non-separating contact; and

[0171] The contact between the downhole tool with extreme bending and the side of the second connector closest to the downhole tool with extreme bending is a bonded contact; the contact between the downhole tool with extreme bending and the middle part of the second connector is a non-separating contact; the contact between the downhole tool with extreme bending and the end face of the second connector away from the downhole tool with extreme bending is a non-separating contact.

[0172] Therefore, it can be seen that the stress calculation device for downhole tools passing through curved well sections according to this embodiment can effectively simulate the actual bending conditions of downhole tools and solve for stress values ​​by deriving displacement functions, setting boundary conditions and loading displacement functions in finite element software.

[0173] Example 3

[0174] According to Embodiment 3 of the present invention, a non-volatile computer storage medium is provided, the computer storage medium storing at least one executable instruction, which can execute the method in any of the above method embodiments.

[0175] Executable instructions can specifically be used to cause the processor to perform the following operations:

[0176] Based on the actual working conditions of the downhole tool, determine whether the bending of the downhole tool is normal bending or extreme bending;

[0177] If the bending of the downhole tool is a conventional bending, then construct the first displacement function of the downhole tool with conventional bending;

[0178] The analysis was performed by loading the first displacement function using finite element software.

[0179] If the bending of the downhole tool is a limiting bending, then construct the second displacement function of the downhole tool for limiting bending; and

[0180] The analysis was performed by loading a second displacement function using finite element software.

[0181] In one alternative implementation, the executable instructions may specifically be used to cause the processor to perform the following operations:

[0182] The first displacement function of a downhole tool under conventional bending is constructed based on a computational model of a simply supported beam subjected to concentrated forces; and

[0183] The second displacement function of the downhole tool under extreme bending is constructed based on the constant curvature circle model.

[0184] In one alternative implementation, the executable instructions may specifically be used to cause the processor to perform the following operations:

[0185] The maximum deflection of a conventionally curved downhole tool is calculated based on the geometric relationship between the conventionally curved downhole tool and the curved well section.

[0186] Calculation of concentrated forces on a simply supported beam under concentrated force based on a computational model; and

[0187] Based on the concentrated force borne by a conventionally curved downhole tool, the deflection equation of the conventionally curved downhole tool is determined, and the displacement function of any point on the conventionally curved downhole tool is obtained.

[0188] In one alternative implementation, the executable instructions may specifically be used to cause the processor to perform the following operations:

[0189] Set the first boundary conditions for conventionally curved downhole tools;

[0190] Finite element mesh generation was performed on a conventionally curved downhole tool using finite element software.

[0191] Obtain the stresses experienced by a conventionally bent downhole tool corresponding to each finite element mesh; and

[0192] To obtain the maximum stress that a conventionally bent downhole tool can withstand.

[0193] In one alternative implementation, the executable instructions may specifically be used to cause the processor to perform the following operations:

[0194] A first displacement function is applied along the longitudinal axis of a conventionally curved downhole tool;

[0195] The degrees of freedom in the horizontal and vertical directions of a conventionally curved downhole tool are set to 0.

[0196] The contact between the conventionally curved downhole tool and the side of the first connector closest to the conventionally curved downhole tool is a bonded contact; the contact between the conventionally curved downhole tool and the middle portion of the first connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the first connector furthest from the conventionally curved downhole tool is a non-separating contact; and

[0197] The contact between the conventionally curved downhole tool and the side of the second connector closest to the conventionally curved downhole tool is a binding contact; the contact between the conventionally curved downhole tool and the middle part of the second connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the second connector furthest from the conventionally curved downhole tool is a non-separating contact.

[0198] In one alternative implementation, the executable instructions may specifically be used to cause the processor to perform the following operations:

[0199] Set the second boundary condition for the downhole tool to limit bending;

[0200] Finite element mesh generation was performed on the downhole tool under extreme bending using finite element software.

[0201] Obtain the stresses experienced by the downhole tool under extreme bending, corresponding to each finite element mesh; and

[0202] The maximum stress that a downhole tool can withstand when it reaches its limit of bending.

[0203] In one alternative implementation, the executable instructions may specifically be used to cause the processor to perform the following operations:

[0204] A second displacement function is applied along the longitudinal axis of the downhole tool under extreme bending.

[0205] The degrees of freedom in the horizontal and vertical directions of the downhole tool under extreme bending are set to 0;

[0206] The contact between the downhole tool with its extreme bending limit and the side of the first connector closest to the extreme bending limit is a bonded contact; the contact between the downhole tool with its extreme bending limit and the middle portion of the first connector is a non-separating contact; the contact between the downhole tool with its extreme bending limit and the end face of the first connector furthest from the extreme bending limit is a non-separating contact; and

[0207] The contact between the downhole tool with extreme bending and the side of the second connector closest to the downhole tool with extreme bending is a bonded contact; the contact between the downhole tool with extreme bending and the middle part of the second connector is a non-separating contact; the contact between the downhole tool with extreme bending and the end face of the second connector away from the downhole tool with extreme bending is a non-separating contact.

[0208] Therefore, it can be seen that the stress calculation method of downhole tools passing through curved well sections according to this embodiment, by deriving the displacement function, setting boundary conditions and loading the displacement function in the finite element software, can well simulate the actual bending condition of the downhole tool and thus solve the stress value.

[0209] Example 4

[0210] Figure 13 The diagram shows a structural schematic of a computing device according to Embodiment 4 of the present invention. The specific embodiments of the present invention do not limit the specific implementation of the computing device.

[0211] like Figure 13 As shown, the computing device may include: a processor 302, a communications interface 304, a memory 306, and a communications bus 308.

[0212] The processor 302, communication interface 304, and memory 306 communicate with each other via communication bus 308. Communication interface 304 is used to communicate with other network elements such as clients or other servers. The processor 302 executes program 310, specifically performing the relevant steps in the above method embodiments.

[0213] Specifically, program 310 may include program code that includes computer operation instructions.

[0214] Processor 302 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention. The computing device may include one or more processors of the same type, such as one or more CPUs; or it may include processors of different types, such as one or more CPUs and one or more ASICs.

[0215] Memory 306 is used to store program 310. Memory 306 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0216] Specifically, program 310 can be used to cause processor 302 to perform the following operations:

[0217] Based on the actual working conditions of the downhole tool, determine whether the bending of the downhole tool is normal bending or extreme bending;

[0218] If the bending of the downhole tool is a conventional bending, then construct the first displacement function of the downhole tool with conventional bending;

[0219] The analysis was performed by loading the first displacement function using finite element software.

[0220] If the bending of the downhole tool is a limiting bending, then construct the second displacement function of the downhole tool for limiting bending; and

[0221] The analysis was performed by loading a second displacement function using finite element software.

[0222] In one alternative implementation, program 310 may specifically be used to cause processor 302 to perform the following operations:

[0223] The first displacement function of a downhole tool under conventional bending is constructed based on a computational model of a simply supported beam subjected to concentrated forces; and

[0224] The second displacement function of the downhole tool under extreme bending is constructed based on the constant curvature circle model.

[0225] In one alternative implementation, program 310 may specifically be used to cause processor 302 to perform the following operations:

[0226] The maximum deflection of a conventionally curved downhole tool is calculated based on the geometric relationship between the conventionally curved downhole tool and the curved well section.

[0227] Calculation of concentrated forces on a simply supported beam under concentrated force based on a computational model; and

[0228] Based on the concentrated force borne by a conventionally curved downhole tool, the deflection equation of the conventionally curved downhole tool is determined, and the displacement function of any point on the conventionally curved downhole tool is obtained.

[0229] In one alternative implementation, program 310 may specifically be used to cause processor 302 to perform the following operations:

[0230] Set the first boundary conditions for conventionally curved downhole tools;

[0231] Finite element mesh generation was performed on a conventionally curved downhole tool using finite element software.

[0232] Obtain the stresses experienced by a conventionally bent downhole tool corresponding to each finite element mesh; and

[0233] To obtain the maximum stress that a conventionally bent downhole tool can withstand.

[0234] In one alternative implementation, program 310 may specifically be used to cause processor 302 to perform the following operations:

[0235] A first displacement function is applied along the longitudinal axis of a conventionally curved downhole tool;

[0236] The degrees of freedom in the horizontal and vertical directions of a conventionally curved downhole tool are set to 0.

[0237] The contact between the conventionally curved downhole tool and the side of the first connector closest to the conventionally curved downhole tool is a bonded contact; the contact between the conventionally curved downhole tool and the middle portion of the first connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the first connector furthest from the conventionally curved downhole tool is a non-separating contact; and

[0238] The contact between the conventionally curved downhole tool and the side of the second connector closest to the conventionally curved downhole tool is a binding contact; the contact between the conventionally curved downhole tool and the middle part of the second connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the second connector furthest from the conventionally curved downhole tool is a non-separating contact.

[0239] In one alternative implementation, program 310 may specifically be used to cause processor 302 to perform the following operations:

[0240] Set the second boundary condition for the downhole tool to limit bending;

[0241] Finite element mesh generation was performed on the downhole tool under extreme bending using finite element software.

[0242] Obtain the stresses experienced by the downhole tool under extreme bending, corresponding to each finite element mesh; and

[0243] The maximum stress that a downhole tool can withstand when it reaches its limit of bending.

[0244] In one alternative implementation, program 310 may specifically be used to cause processor 302 to perform the following operations:

[0245] A second displacement function is applied along the longitudinal axis of the downhole tool under extreme bending.

[0246] The degrees of freedom in the horizontal and vertical directions of the downhole tool under extreme bending are set to 0;

[0247] The contact between the downhole tool with its extreme bending limit and the side of the first connector closest to the extreme bending limit is a bonded contact; the contact between the downhole tool with its extreme bending limit and the middle portion of the first connector is a non-separating contact; the contact between the downhole tool with its extreme bending limit and the end face of the first connector furthest from the extreme bending limit is a non-separating contact; and

[0248] The contact between the downhole tool with extreme bending and the side of the second connector closest to the downhole tool with extreme bending is a bonded contact; the contact between the downhole tool with extreme bending and the middle part of the second connector is a non-separating contact; the contact between the downhole tool with extreme bending and the end face of the second connector away from the downhole tool with extreme bending is a non-separating contact.

[0249] Therefore, it can be seen that the stress calculation method of downhole tools passing through curved well sections according to this embodiment, by deriving the displacement function, setting boundary conditions and loading the displacement function in the finite element software, can well simulate the actual bending condition of the downhole tool and thus solve the stress value.

[0250] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0251] Similarly, it should be understood that, in order to simplify the invention and aid in understanding one or more of the various inventive aspects, features of the embodiments of the invention are sometimes grouped together in a single embodiment, figure, or description thereof in the above description of exemplary embodiments of the invention. However, this disclosure should not be construed as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as reflected in the following claims, inventive aspects lie in fewer than all features of a single foregoing disclosed embodiment. Therefore, the claims following the detailed description are hereby expressly incorporated into this detailed description, wherein each claim itself is a separate embodiment of the invention.

[0252] Those skilled in the art will understand that modules in the device of the embodiments can be adaptively changed and placed in one or more devices different from that embodiment. Modules, units, or components in the embodiments can be combined into a single module, unit, or component, and further, they can be divided into multiple sub-modules, sub-units, or sub-components. Except where at least some of such features and / or processes or units are mutually exclusive, any combination can be used to combine all features disclosed in this specification (including the accompanying claims, abstract, and drawings) and all processes or units of any method or device so disclosed. Unless expressly stated otherwise, each feature disclosed in this specification (including the accompanying claims, abstract, and drawings) may be replaced by an alternative feature that serves the same, equivalent, or similar purpose.

[0253] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0254] It should be noted that the above embodiments are illustrative of the invention and not restrictive, and that those skilled in the art can devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses should not be construed as limiting the claims. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention can be implemented by means of hardware comprising several different elements and by means of a suitably programmed computer. In the unit claims enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, and third, etc., does not indicate any order. These words can be interpreted as names. The steps in the above embodiments, unless otherwise specified, should not be construed as limiting the order of execution.

Claims

1. A method for calculating the stress of downhole tools in curved well sections, characterized in that, include: Based on the actual working conditions of the downhole tool, determine whether the bending of the downhole tool is a normal bending or an extreme bending. If, when a downhole tool passes through a curved section, both ends of the downhole tool are restricted by the upper well wall, and the middle part of the downhole tool is restricted by the lower well wall, then the bending of the downhole tool is judged as normal bending. If, when the downhole tool passes through a curved section, it encounters resistance during descent or jamming during descent, applying axial force to the downhole tool will cause it to bend against the casing wall, then the bending of the downhole tool is judged as extreme bending. If the bending of the downhole tool is conventional bending, then the first displacement function of the downhole tool under conventional bending is constructed based on the calculation model of a simply supported beam subjected to concentrated force. The first displacement function was loaded and analyzed using finite element software. If the bending of the downhole tool is a limiting bending, then a second displacement function of the downhole tool for limiting bending is constructed based on the constant curvature circle model; and The second displacement function was loaded and analyzed using finite element software.

2. The calculation method according to claim 1, characterized in that, The calculation model based on a simply supported beam subjected to concentrated forces constructs the first displacement function of the conventionally bending downhole tool, further including: The maximum deflection of the conventionally curved downhole tool is calculated based on the geometric relationship between the conventionally curved downhole tool and the curved well section. The concentrated force borne by the conventionally bent downhole tool is calculated based on the calculation model of the simply supported beam subjected to concentrated force; and Based on the concentrated force borne by the conventionally curved downhole tool, the deflection equation of the conventionally curved downhole tool is determined, and the displacement function of any point of the conventionally curved downhole tool is obtained.

3. The calculation method according to claim 1, characterized in that, The step of analyzing the first displacement function using finite element software further includes: Set the first boundary conditions for the conventionally curved downhole tool; The conventionally curved downhole tool was meshed using the finite element software. Obtain the stresses experienced by the conventionally bent downhole tool corresponding to each finite element mesh; and The maximum stress that the conventionally bent downhole tool can withstand is obtained.

4. The calculation method according to claim 3, characterized in that, The first boundary condition for setting conventional curved downhole tools further includes: The first displacement function is applied in the longitudinal direction of the conventionally curved downhole tool; The degrees of freedom in the horizontal and vertical directions of the conventionally curved downhole tool are set to 0. The contact between the conventionally curved downhole tool and the side of the first connector closest to the conventionally curved downhole tool is a bonded contact; the contact between the conventionally curved downhole tool and the middle portion of the first connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the first connector furthest from the conventionally curved downhole tool is a non-separating contact; and The contact between the conventionally curved downhole tool and the second connector on the side closest to the conventionally curved downhole tool is a binding contact; the contact between the conventionally curved downhole tool and the middle portion of the second connector is a non-separating contact; the contact between the conventionally curved downhole tool and the end face of the second connector on the side furthest from the conventionally curved downhole tool is a non-separating contact.

5. The calculation method according to claim 1, characterized in that, The analysis by loading the second displacement function using finite element software further includes: Set the second boundary conditions for the downhole tool with the extreme bending; The downhole tool subjected to extreme bending was meshed using the finite element software. Obtain the stresses experienced by the downhole tool under extreme bending, corresponding to each finite element mesh; and The maximum stress that the downhole tool under the ultimate bending condition is obtained.

6. The calculation method according to claim 5, characterized in that, The second boundary condition for the downhole tool with extreme bending further includes: The second displacement function is applied in the longitudinal direction of the downhole tool under extreme bending. The degrees of freedom in the horizontal and vertical directions of the downhole tool with extreme bending are set to 0. The contact between the extreme bending downhole tool and the side of the first connector closest to the extreme bending downhole tool is a bonded contact; the contact between the extreme bending downhole tool and the middle portion of the first connector is a non-separating contact; the contact between the extreme bending downhole tool and the end face of the first connector furthest from the extreme bending downhole tool is a non-separating contact; and The contact between the extreme bending downhole tool and the side of the second connector closest to the extreme bending downhole tool is a binding contact; the contact between the extreme bending downhole tool and the middle portion of the second connector is a non-separating contact; the contact between the extreme bending downhole tool and the end face of the second connector away from the extreme bending downhole tool is a non-separating contact.

7. A device for calculating the stress of downhole tools in curved well sections, characterized in that, The computing device includes: The judgment module is adapted to determine whether the bending of the downhole tool is a normal bending or an extreme bending based on the actual working conditions of the downhole tool. If the two ends of the downhole tool are restricted by the upper well wall and the middle part of the downhole tool is restricted by the lower well wall when passing through the bending section, the bending of the downhole tool is judged as a normal bending. If the downhole tool encounters resistance when lowering or gets stuck when lifting through the bending section, and applying axial force to the downhole tool will cause it to bend against the casing wall, the bending of the downhole tool is judged as an extreme bending. The first construction module is adapted to construct the first displacement function of the downhole tool under conventional bending based on the calculation model of a simply supported beam subjected to concentrated force if the bending of the downhole tool is conventional bending. The first analysis module is suitable for performing analysis by loading the first displacement function using finite element software; The second construction module is adapted to construct a second displacement function of the downhole tool under extreme bending based on an isocurvature circle model if the bending of the downhole tool is an extreme bending; and The second analysis module is suitable for performing analysis by loading the second displacement function using finite element software.

8. A computing device, comprising: The processor, memory, communication interface, and communication bus are provided, wherein the processor, memory, and communication interface communicate with each other via the communication bus. The memory is used to store at least one executable instruction that causes the processor to perform an operation corresponding to the method for calculating the stress of downhole tools through curved well sections as described in any one of claims 1-6.

9. A computer storage medium storing at least one executable instruction that causes a processor to perform an operation corresponding to the method for calculating the stress of a downhole tool through a curved well section as described in any one of claims 1-6.

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