Methods and apparatus for determining buckling phenomena in tubular columns, electronic equipment and storage media

Abstract

This disclosure relates to a method, apparatus, electronic device, and storage medium for determining buckling phenomena in a tubing string, belonging to the field of piping. The method includes: determining the stress and moment of a micro-element of the tubing string to be tested, wherein the stress of the micro-element is the resultant force of gravity, support reaction force, friction force, and pressure acting on the micro-element, and the moment of the micro-element is the bending moment and torque of the micro-element; determining the equilibrium differential equation of the micro-element based on the stress and moment of the micro-element, wherein the equilibrium differential equation of the micro-element includes the stress equilibrium differential equation and the moment equilibrium differential equation of the micro-element; determining the buckling differential equation of the micro-element based on the equilibrium equation of the micro-element, wherein the buckling differential equation of the micro-element represents the total force and total deformation of the micro-element; and determining whether buckling phenomena have occurred in the tubing string to be tested based on the buckling differential equation of the micro-element.

Description

Technical Field

[0001] This disclosure relates to the field of piping, and in particular to a method and apparatus for determining buckling phenomena in a tubular string, electronic equipment, and storage medium. Background Technology

[0002] An oil well consists of casing and tubing. The casing is typically cemented to the wellbore, and the tubing is located inside the casing. The tubing string is made of multiple welded pipes, through which extracted oil or gas is transported to the surface.

[0003] In recent years, with the development of the oil and gas industry, oil wells have become deeper and deeper, and the temperature and pressure on the tubing strings have become higher and higher. Under high temperature and high pressure, the tubing strings may bend and twist, a phenomenon known as tubing string buckling.

[0004] Tubing buckling can cause deviations in the tubing path, increase the stress on the tubing, and easily lead to tubing damage, affecting the normal production of the oil field. Summary of the Invention

[0005] This disclosure provides a method, apparatus, electronic device, and storage medium for determining the buckling phenomenon of a tubing string. The technical solution is as follows:

[0006] This disclosure provides a method for determining buckling phenomena in a tubular column. The method includes: determining the stress and moment of a micro-element of the tubular column under test, wherein the stress of the micro-element is the resultant force of gravity, support reaction force, friction force, and pressure acting on the micro-element, and the moment of the micro-element is the bending moment and torque of the micro-element; determining the equilibrium differential equation of the micro-element based on the stress and moment of the micro-element, wherein the equilibrium differential equation of the micro-element includes the stress equilibrium differential equation and the moment equilibrium differential equation of the micro-element; determining the buckling differential equation of the micro-element based on the equilibrium equation of the micro-element, wherein the buckling differential equation of the micro-element represents the total force and total deformation of each micro-element of the tubular column under test; and determining whether buckling phenomena have occurred in the tubular column under test based on the buckling differential equation of the micro-element.

[0007] In one implementation of this disclosure, the stress of the micro-element includes components in three directions within the body coordinate system. Determining the stress of the micro-element of the test column includes: determining the gravity, support reaction force, friction force, and pressure acting on each micro-element of the test column; decomposing each of the gravity, support reaction force, friction force, and pressure into components in three directions within the body coordinate system; and combining the components of gravity, support reaction force, friction force, and pressure in each direction for each micro-element to obtain the stress components of each micro-element in the three directions within the body coordinate system.

[0008] In one implementation of this disclosure, each of the gravity, the support reaction force, the frictional force, and the pressure is decomposed into components in three directions within the body coordinate system, including:

[0009] The gravity can be decomposed according to the following formula:

[0010] G = q τ e τ +q n e n +q b e b

[0011] in:

[0012] G—gravity, unit: Newton;

[0013] e τ —A direction vector within natural coordinates;

[0014] q τ —Gravity in e τ The component in the direction in which it is located, in Newtons;

[0015] e n —A direction vector within natural coordinates;

[0016] q n —Gravity in e n The component in the direction in which it is located, in Newtons;

[0017] e b —A direction vector within natural coordinates;

[0018] q b —Gravity in e b The component in the direction in which it is located, in Newtons;

[0019] The support reaction force can be decomposed according to the following formula:

[0020]

[0021] in,

[0022] —A reaction force, unit: Newton;

[0023] N—the component of the support reaction force in one direction of the natural coordinate system, in Newtons;

[0024] β—Coefficient of thermal expansion of the material of the test column, in meters per degree Celsius;

[0025] e2—a direction vector of natural coordinates;

[0026] e3—a direction vector of natural coordinates;

[0027] The frictional force includes Coulomb friction and viscous friction, which can be decomposed according to the following formula:

[0028] f kl =±f kl Ne1±f hx Nsinβe2±f hx Ncosβe3

[0029] in,

[0030] f kl — Coulomb friction, unit: Newton;

[0031] e1—a direction vector of natural coordinates;

[0032] f hx —The coefficient of circumferential friction between the test tubing and the inner wall of the casing;

[0033] The viscous friction force can be decomposed according to the following formula:

[0034] f nz =±(S) i τ fi +S o τ fo )e1

[0035] in,

[0036] f nz —Viscous friction, unit: Newton;

[0037] S i —Circumference of the inner wall of the section of the pipe to be tested, in meters;

[0038] τ fi —Viscous shear stress between the fluid and the inner wall of the test tube, in Newtons per square meter;

[0039] S o —Circumference of the outer wall of the section of the pipe to be tested, in meters;

[0040] τ fo —Viscous shear stress between the fluid and the outer wall of the test tube, in Newtons per square meter;

[0041] The pressure can be decomposed according to the following formula:

[0042] F fb =(Ffbi τ -Ffboτ )e τ +(Ffbi n -Ffbo n )e n +(Ffbi b -Ffbo b )e b

[0043] in,

[0044] F fb —Pressure, unit: Newton;

[0045] Ffbi τ —The first distributed load of pressure in e τ Component in direction, unit: Newton;

[0046] Ffbo τ —The second distributed load of pressure in e τ Component in direction, unit: Newton;

[0047] Ffbi n —The first distributed load of pressure in e n Component in direction, unit: Newton;

[0048] Ffbo n —The second distributed load of pressure in e n Component in direction, unit: Newton;

[0049] Ffbi b —The first distributed load of pressure in e b Component in direction, unit: Newton;

[0050] Ffbo b —The second distributed load of pressure in e b Component in direction, unit: Newton.

[0051] In one implementation of this disclosure, the stress equilibrium differential equation of the infinitesimal element is:

[0052]

[0053] in,

[0054] F1—Axial force, unit: Newton;

[0055] F2—Shear force in the direction of natural coordinate e2, unit: Newton;

[0056] F3—Shear force in the direction of natural coordinate e3, unit: Newton;

[0057] F w1—Stress in the natural coordinate e1 direction, in Newtons;

[0058] F w2 —Stress in the natural coordinate e2 direction, in Newtons;

[0059] F w3 —Stress in the natural coordinate e3 direction, in Newtons;

[0060] k τ —Natural coordinates e τ Change in curvature in a direction, unit: negative first meter;

[0061] k n —Natural coordinates e n Change in curvature in a direction, unit: negative first meter;

[0062] k b —Natural coordinates e b Change in curvature in a direction, unit: negative first meter;

[0063] The torque balance differential equation of the infinitesimal element is:

[0064]

[0065] in,

[0066] M1—Torque in the direction of natural coordinate e1, unit: Newton-meter;

[0067] M2—Torque in the direction of natural coordinate e2, unit: Newton-meter;

[0068] M3 — Torque in the direction of natural coordinate e3, unit: Newton-meter.

[0069] In one implementation of this disclosure, the buckling differential equation of the micro-element includes a stress buckling differential equation and a moment buckling differential equation. Determining the buckling differential equation of the micro-element based on its equilibrium equation includes: determining the strain of the micro-element based on the relationship between stress and strain and the stress of the micro-element; determining the curvature change of the micro-element based on the relationship between moment and curvature change and the moment of the micro-element; substituting the strain of the micro-element into the stress equilibrium equation of the micro-element to obtain the stress buckling differential equation of the micro-element; and substituting the curvature change of the micro-element into the moment equilibrium equation to obtain the moment buckling differential equation of the micro-element.

[0070] In one implementation of this disclosure, the change in curvature of the infinitesimal element is substituted into the moment balance equation to obtain the moment buckling differential equation of the infinitesimal element. This includes: substituting the change in curvature of the infinitesimal element into the moment balance equation to obtain a first equation; differentiating the first equation to obtain a relationship between the moment of the infinitesimal element and the change in curvature and the elastic modulus of the infinitesimal element, wherein the relationship is the moment buckling differential equation of the infinitesimal element.

[0071] In one implementation of this disclosure, determining whether the test column has buckled based on the buckling differential equation of the micro-element includes: determining the total force and total deformation of each micro-element of the test column based on the buckling differential equation of the micro-element; and determining whether the test column has buckled based on the total force and total deformation of each micro-element.

[0072] On the other hand, embodiments of this disclosure provide a device for determining buckling phenomena of a tubing column. The device includes: a first determining module configured to determine the stress and moment of a micro-element of the tubing column to be tested, wherein the stress of the micro-element is the resultant force of gravity, support reaction force, friction force, and pressure acting on the micro-element, and the moment of the micro-element is the bending moment and torque of the micro-element; a second determining module configured to determine the equilibrium differential equation of the micro-element based on the stress and moment of the micro-element, wherein the equilibrium differential equation of the micro-element includes the stress equilibrium differential equation and the moment equilibrium differential equation of the micro-element; a third determining module configured to determine the buckling differential equation of the micro-element based on the equilibrium equation of the micro-element, wherein the buckling differential equation of the micro-element represents the total force and total deformation of each micro-element of the tubing column to be tested; and a fourth determining module configured to determine whether buckling phenomena occur in the tubing column to be tested based on the buckling differential equation of the micro-element.

[0073] On the other hand, embodiments of this disclosure provide an electronic device, the electronic device comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to perform the buckling phenomenon determination method of the column as described in any of the preceding aspects.

[0074] On the other hand, embodiments of this disclosure provide a computer-readable storage medium storing a computer program, which is executed by a processor to implement the method for determining the buckling phenomenon of a tubular column as described in any of the above aspects.

[0075] The beneficial effects of the technical solutions provided in this disclosure are:

[0076] In this embodiment, by performing individual stress and strain analysis on each micro-element of the test string, a buckling differential equation for each micro-element is established. Then, based on the buckling differential equation, the total force and total deformation of each micro-element are determined, thereby determining whether buckling has occurred in the test string. This method can determine whether buckling has occurred in the downhole test string. If buckling has occurred, the operators can then straighten the downhole string based on the force and deformation, preventing damage to the tubing and affecting normal oilfield production. Attached Figure Description

[0077] To more clearly illustrate the technical solutions in the embodiments of this disclosure, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1 This is a flowchart of a method for determining the buckling phenomenon of a tubular column according to an embodiment of this disclosure;

[0079] Figure 2 This is a flowchart of a method for determining the buckling phenomenon of a tubular column according to an embodiment of this disclosure;

[0080] Figure 3 This is a diagram illustrating the buckling phenomenon of a tubular column in the X direction, provided in an embodiment of this disclosure.

[0081] Figure 4 This is a diagram illustrating the buckling phenomenon of a tubular column in the Y direction, provided in an embodiment of this disclosure.

[0082] Figure 5 This is a schematic diagram of the structure of a device for determining the buckling phenomenon of a tubular column provided in an embodiment of this disclosure;

[0083] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this disclosure. Detailed Implementation

[0084] To make the objectives, technical solutions, and advantages of this disclosure clearer, the embodiments of this disclosure will be described in further detail below with reference to the accompanying drawings.

[0085] During downhole operation, tubing strings experience piston effect, bulging effect, temperature effect, bending effect, and friction effect. These effects cause changes in the length of the tubing string, resulting in strain, which in turn contributes to the buckling of the tubing string. Before introducing the method provided in the embodiments of this disclosure, the impact of each effect on the buckling of the tubing string will be briefly explained to facilitate a better understanding of the method provided in the embodiments of this disclosure.

[0086] Oil wells and gas wells consist of tubing, casing, and packers. The tubing is located inside the casing, and the packers are located in the annulus between the tubing and casing.

[0087] 1. Piston effect

[0088] If the tubing string is divided into n stages from bottom to top according to its connection configuration, where n is a positive integer, then the piston force at the bottom of the first stage tubing string is:

[0089] F hs1 =(A p -A i1 )P i1 -(A p -A o1 )P o1 (1)

[0090] In formula (1):

[0091] F hs1 —The piston force at the bottom of the first-stage tubing string, in Newtons;

[0092] A p —Cross-sectional area of ​​the packer sealing cavity, unit: square millimeters;

[0093] A i1 —Cross-sectional area of ​​the first-stage tubing string, in square millimeters;

[0094] P i1 —Pressure inside the tubing string at the packer, unit: megapascals;

[0095] A o1 —Cross-sectional area of ​​the first section of the tubing string, unit: square millimeters;

[0096] P o1 — Annular fluid pressure at the packer, unit: megapascals.

[0097] The piston force at the bottom of the second-stage tubing string is:

[0098] F hs2 =F hs1 +(A i1 -A i2 )P i2 -(A o1 -A o2 )P o2 -ρ g gL1A s1 (2)

[0099] In formula (2):

[0100] F hs2—The piston force at the bottom of the second-stage tubing string, in Newtons;

[0101] A i2 —The area enclosed by the inner diameter of the second-stage tubing string, in square millimeters;

[0102] P i2 —Inner pressure at the bottom of the second-stage tubing string, unit: megapascals;

[0103] A o2 —The area enclosed by the outer diameter of the second-stage tubing string, in square millimeters;

[0104] P o2 —Annular fluid pressure at the bottom of the second-stage tubing string, unit: megapascals;

[0105] ρ g —Annular fluid density at the bottom of the tubing string, in grams per cubic millimeter;

[0106] g — acceleration due to gravity, unit: meters per second squared;

[0107] L1—Length of the first-stage tubing string, in meters;

[0108] A s1 —Cross-sectional area of ​​the first-stage tubing string, in square millimeters.

[0109] ...and so on, therefore:

[0110] The piston force at the bottom of the nth stage tubing string is:

[0111] F hsn =F hs(n-1) +(A i(n-1) -A in )P in -(A o(n-1) -A on )P on -ρ g gL (n-1) A s(n-1) (3)

[0112] In formula (3):

[0113] F hsn —The piston force at the bottom of the nth stage tubing string, in Newtons;

[0114] F hs(n-1) —The piston force at the bottom of the (n-1)th stage tubing string, in Newtons;

[0115] A i(n-1) —The area enclosed by the inner diameter of the (n-1)th stage tubing string, in square millimeters;

[0116] A in —The area enclosed by the inner diameter of the nth stage tubing string, in square millimeters;

[0117] P in —Inner pressure at the bottom of the nth stage tubing string, unit: megapascals;

[0118] A o(n-1) —The area enclosed by the outer diameter of the (n-1)th stage tubing string, in square millimeters;

[0119] A on —The area enclosed by the outer diameter of the nth stage tubing string, in square millimeters;

[0120] P on —Annular fluid pressure at the bottom of the nth stage tubing string, in megapascals;

[0121] L (n-1) —Length of the (n-1)th stage tubing string, in meters;

[0122] A s(n-1) —Cross-sectional area of ​​the (n-1)th stage tubing string, in square millimeters.

[0123] If parameters such as oil pressure, casing, or fluid density within the well change, then the change in piston force ΔF of the nth stage tubing string will be significant. hsn It can be represented as:

[0124] F hsn =ΔF hs(n-1) +(A i(n-1) -A in )ΔP in -(A o(n-1 )-A on )ΔP on (4)

[0125] In formula (4):

[0126] ΔF hs(n-1) —The change in piston force of the tubing string in the (n-1)th stage, in Newtons;

[0127] ΔP in —The change in internal pressure at the bottom of the nth stage tubing string, in megapascals;

[0128] ΔP 0n —The change in annular fluid pressure at the bottom of the nth stage tubing string, in megapascals.

[0129] The change in piston force ΔF1 throughout the tubing string can be expressed as:

[0130]

[0131] The change in the length of the nth stage tubing string ΔL hsn for:

[0132]

[0133] In formula (6):

[0134] L n —Length of the nth stage tubing string, in meters;

[0135] E—Elastic modulus of tubing string, unit: megapascals.

[0136] From formula (6), the change in the length of the entire tubing string ΔL1 caused by the piston effect is:

[0137]

[0138] 2. Expansion effect

[0139] The tubing string bulges under the pressure of internal and external fluids, and changes in the fluid pressure inside the string will cause the tubing string to lengthen or shorten. According to the thick-walled cylinder theory of mechanics of materials, the radial stress and circumferential stress at any position along the axial direction of the tubing string can be expressed by formulas (8) and (9), respectively:

[0140]

[0141] In formula (8):

[0142] σ r The radial stress on the tubing string at point s, in megapascals;

[0143] r i —Radius at any point on the cross-section of the tubing string, in millimeters;

[0144] p i (s)—The internal pressure of the tubing string at point s, in megapascals;

[0145] r o —Outer radius of the tubing string, in millimeters;

[0146] p o (s)—The external pressure on the tubing string at point s, in megapascals;

[0147] r—The average radius of the tubing string, in millimeters.

[0148]

[0149] In formula (9):

[0150] σ θ —The circumferential stress on the tubing string at point s, in megapascals.

[0151] When the internal pressure of the tubing string changes, the axial strain change of the tubing string can be obtained from equations (8) and (9) combined with Hooke's law as follows:

[0152]

[0153] In formula (10):

[0154] μ—Poisson's ratio of the tubing string;

[0155] Δσ r (s)—The change in radial stress on the tubing string at point s, in megapascals;

[0156] Δσ θ (s)—The change in circumferential stress on the tubing string at point s, in megapascals;

[0157] Δp i (s) — The change in internal pressure at point s of the tubing string, in megapascals;

[0158] Δp0(s) — Change in annular fluid pressure at point s in the tubing string, in megapascals.

[0159] The length change ΔL2(s) of the tubing string below any point s under the influence of the bulging effect is:

[0160]

[0161] In formula (11):

[0162] L sx —The length of the tubing string below point s, in meters.

[0163] When the wellbore pressure changes, the bulging force ΔF2(s) of the tubing string below any position s can be expressed as:

[0164]

[0165] In formula (12):

[0166] A o —The area enclosed by the outer diameter of the completion string, in square meters;

[0167] A i —The area enclosed by the inner diameter of the completion string, in square meters.

[0168] The length change ΔL2 and the bulging force ΔF2 of the entire tubing string under the bulging effect are respectively:

[0169]

[0170] In formula (13):

[0171] L 总 —Total length of the downhole tubing string, in meters.

[0172]

[0173] 3. Temperature effect

[0174] When the temperature inside the wellbore changes, the temperature effect causes the tubing string to elongate or shorten. The change in tubing string length ΔL3 below any point s due to the temperature effect is:

[0175]

[0176] In formula (15):

[0177] β—Coefficient of thermal expansion of the material, unit: meters per degree Celsius;

[0178] T h (s) — Temperature at point s in the tubing string under current operating conditions, in degrees Celsius;

[0179] T q (s) — Temperature at point s in the tubing string under reference operating conditions, in degrees Celsius.

[0180] The temperature effect force ΔF3 experienced by the tubing string below any point s due to temperature effect is:

[0181]

[0182] The length change ΔL3 and temperature-induced stress ΔF3 of the entire tubing string under temperature effects are as follows:

[0183]

[0184]

[0185] 4. Bending effect

[0186] The pressure acts not only perpendicularly along the axis of the tubing string to the sealing tube and the tubing string at the packer, but also horizontally on the entire wall of the tubing string. If the internal pressure of the tubing string above the packer is greater than the pressure in the annular space at that location, the tubing string inside the casing will undergo helical bending.

[0187] There are two types of helical bending: elastic helical bending and permanent helical bending. The following section introduces the influence of bending effect on the buckling phenomenon of tubing strings.

[0188] (1) No fluid inside or outside the tubing string

[0189] 1) The distance n from the bottom of the tubing to the neutral point:

[0190]

[0191] In formula (19):

[0192] F—Axial force on the end face of the tubing, unit: Newton;

[0193] W—Weight per unit length of tubing string, in Newtons.

[0194] Wherein: the neutral point is the point where the axial stress is zero. Typically, the tubing bends spirally below the neutral point, and remains straight above the neutral point.

[0195] 2) Pitch h

[0196]

[0197] In formula (20):

[0198] I—the moment of inertia of the cross-sectional area of ​​the tubing string about its diameter, and:

[0199]

[0200] In formula (21):

[0201] D—Outer diameter of the tubing string, in millimeters;

[0202] d—Inner diameter of the tubing string, unit: millimeters.

[0203] 3) Mathematical model for shortening of tubular columns that produce helical bends

[0204] ① Under the action of force F, the tubular column undergoes a longitudinal shortening Δl z

[0205]

[0206] In formula (22):

[0207] L—Length of tubing string, in meters;

[0208] A s —Cross-sectional area of ​​the tubing string, in square millimeters.

[0209] ② The longitudinal shortening Δl4 below the neutralization point due to the helical bending of the tubing itself

[0210]

[0211] ③ A mechanical model of fictitious forces

[0212] In a packer that allows free movement, the tubing string is filled with fluid, and the pump experiences a fictitious pressure F. f The mathematical model for whether or not the tubing string will undergo helical bending is as follows:

[0213] F f =A P (p i -p0) (24)

[0214] In formula (24):

[0215] p i— Pressure inside the tubing string, unit: Newton;

[0216] p o— External pressure in the tubing string, unit: Newton.

[0217] In formula (24), if F f If F > 0, then the fictitious force is a compressive force, and the tubing string undergoes helical bending. f If the value is ≤0, then the fictitious force is tension, and the tubing string remains straight. The fictitious force is the difference between the actual axial force and the effective axial force.

[0218] (2) Situation where there is fluid inside and outside the tubing string

[0219] 1) Mathematical Model of Fictional Force

[0220] The pressure change inside and outside the tubing string before and after packer setting is Δp i Given Δp0, the mathematical model of its fictitious force is:

[0221] F f =A P (Δp i -Δp0) (25)

[0222] In the presence of fluid, the weight W per unit length of tubing string is:

[0223] W = W s +W i -W0 (26)

[0224] In formula (26):

[0225] W s—The average weight per unit length of tubing string in air (including couplings), in Newtons per meter;

[0226] W i —The weight of fluid per unit length of tubing string, in Newtons per meter;

[0227] W0—The weight of gas displaced from the casing per unit length of tubing string (calculated by outer diameter), in Newtons per meter.

[0228] 2) Mathematical model of neutralization point location and pitch

[0229] When gas is present in the well, the location of the neutralization point and the pitch of the tubing string are required. This necessitates deriving the fictitious force F from formula (25). f .

[0230] Neutral point:

[0231]

[0232] Pitch:

[0233]

[0234] 3) Shortening of the tubing due to helical bending Δl4

[0235] In the presence of fluid, the shortening Δl4 caused by the shortening radius due to helical bending of the tubing is:

[0236]

[0237] In formula (29), Δl4 is relative to the initial condition p. i The change in tubing string length when p = p0. If Δp0 > Δp i If so, spiral bending will not occur.

[0238] (3) The neutralization point is above the upper end of the tubing.

[0239] When the neutralization point of the tubing above the packer is within the tubing, i.e., when the neutralization point exceeds the tubing (for composite tubing, when it exceeds the same level of tubing), the force F acting on the lower end of the tubing causes a change in tubing length Δl4 as follows:

[0240]

[0241] (4) Permanent spiral bending

[0242] Fluid pressure generates maximum stress only on the inner wall of the tubing string; conversely, bending generates maximum stress only on the outer wall. When both fluid pressure and bending (spiral bending) are present, yielding may occur on the inner and outer walls, but not between them. Based on this principle, to ensure that permanent "spiraling" does not occur after changes in pressure and temperature, inequalities (31) and (32) must be satisfied:

[0243]

[0244] In formula (31):

[0245] s o —The combined stress on the outer wall of the tubing string, in megapascals;

[0246] s—Yield strength, unit: megapascal;

[0247] R—Helix radius when helical bending occurs, in millimeters;

[0248] σ a — Bending stress, unit: Newton;

[0249] σ b —Axial stress, unit: Newton.

[0250]

[0251] In formula (32):

[0252] s i —The combined stress on the inner wall of the tubing string, in megapascals;

[0253] in:

[0254]

[0255] In formula (33):

[0256] —The fictitious pressure exerted on the oil pump.

[0257]

[0258] In formula (34):

[0259] —The force acting on the oil pipe, in Newtons.

[0260] In the above formulas (31) and (32), σ b The sign of the value is determined by the pressure inside and outside the tubing, i.e., by s. o and s iThe value of s determines the magnitude of the value. o If the stress is greater than si, the tubular column will be subjected to external extrusion force, σ b If σb is negative, then if so is less than si, the tubing string is under internal pressure, and σb is positive. However, if the tubing string does not buckle spirally after pressure and temperature changes, the additional axial force caused by thread buckling is 0, then σb is negative. b =0.

[0261] To study the permanent helical bending caused by relaxation force (placing the tubing string on the packer) before pressure and temperature changes, it can be represented as:

[0262]

[0263] (5) Bending effect force

[0264] The stress ΔF4 caused by the change in length of the entire tubing string under bending effect is:

[0265]

[0266] 5. Friction effect

[0267] During operation and production, the tubing string is subjected to both viscous friction and coulombic friction loads. For ultra-deep, high-temperature and high-pressure gas wells, the viscous friction load and coulombic friction load on the tubing string are very large, and in some cases, they are even the main cause of downhole accidents such as tubing string failure and packer setting failure.

[0268] (1) Viscous friction

[0269] The following is a detailed analysis of each flow scenario:

[0270] ① First case

[0271] For conditions such as acid squeezing and positive circulation where the fluid inside the tubing flows downwards and the annular fluid is stationary, the calculation is performed step by step downwards from the wellhead. Considering viscous friction, the fluid pressure at point s inside the tubing is calculated using the following formula:

[0272]

[0273] In formula (37):

[0274] p i (s)—Fluid pressure in the tubing string at point s, unit: megapascals;

[0275] p ci —Wellhead pressure, unit: megapascals;

[0276] L ks —Length of point s inside the tubing string, in meters;

[0277] ρ i —Inner pressure of the tubing string, unit: megapascals;

[0278] α—Well inclination angle, unit: degrees;

[0279] v i —The velocity of fluid flow inside the oil pipe, in meters per second.

[0280] The viscous friction force experienced by the tubing string from the wellhead to point s is:

[0281]

[0282] In formula (38):

[0283] F nf (s) — Viscous friction load on the tubing string from the wellhead to point s, in Newtons.

[0284] ②The second case

[0285] For conditions such as gas production and fluid discharge where the fluid in the tubing flows upwards and the annular fluid is stationary, the calculation is performed step by step upwards from the bottom of the well. Considering viscous friction, the fluid pressure at point s in the tubing string is calculated using formula (39):

[0286]

[0287] In formula (39):

[0288] p cd —Fluid pressure at the bottom of the tubing string, in megapascals;

[0289] v o —The velocity of fluid flow within the annulus, in meters per second.

[0290] The viscous friction force experienced by the tubing string from the bottom of the well to point s is:

[0291]

[0292] ③ The third situation

[0293] For positive circulation systems where the fluid in the tubing flows downwards and the fluid in the annulus flows upwards, the fluid pressure in the tubing is calculated using the method described in the first case. For the fluid pressure in the annulus, the calculation proceeds upwards from the bottom of the well. Considering viscous friction, the fluid pressure at point s in the annulus is calculated using the following formula:

[0294]

[0295] In formula (41):

[0296] rc —Inner diameter of the casing, in millimeters;

[0297] r o —Inner diameter of the oil pipe, unit: millimeters.

[0298] The viscous friction force experienced by the tubing string from the wellhead to point s is:

[0299]

[0300] ④ Fourth situation

[0301] For reverse circulation and other operating conditions where the fluid inside the tubing flows upward and the fluid in the annulus flows downward, the fluid pressure inside the tubing is calculated using the second method. For the fluid pressure in the annulus, the calculation is performed progressively downwards from the wellhead. Considering viscous friction, the fluid pressure at point s in the annulus is calculated using the following formula:

[0302]

[0303] In formula (43):

[0304] p ti — Wellhead casing pressure, unit: megapascals.

[0305] The viscous friction force experienced by the tubing string from the wellhead to point s is:

[0306]

[0307] (2) Coulomb friction

[0308] The normal pressure N between the tubing string and the casing can be calculated based on the relevant model. The Coulomb friction load on the tubing string below any point s at any position is calculated using formula (45):

[0309]

[0310] In formula (45):

[0311] ξ — Direction of Coulomb friction load.

[0312] When Coulomb friction is upward, ξ = -1; when Coulomb friction is downward, ξ = 1.

[0313] During operation and production, changes in wellbore pressure, temperature, and other parameters cause variations in the stress and deformation of the tubing string. The coefficient ξ (ξ) can be positive or negative, and there may even be cases where ξ is positive for some sections and negative for others. Therefore, when calculating the Coulomb friction load under specific operating conditions, a mechanical analysis of the tubing string under those conditions is performed to determine the direction of the tubing string deformation, and then the value of ξ is determined.

[0314] The length change ΔL caused by the Coulomb friction effect of the tubing string kf (s) is:

[0315]

[0316] Coulomb frictional force ΔF of the entire tubing string kf and length change ΔL kf They are respectively:

[0317]

[0318] In formula (47):

[0319] ξ h — indicates the direction of the Coulomb friction load under the current working condition. Coulomb friction is upward, ξ=-1, and Coulomb friction is downward, ξ=1;

[0320] N h —The positive pressure between the completion string and casing under current operating conditions, in Newtons;

[0321] ξ q —Indicates the direction of the Coulomb friction load under the previous working condition;

[0322] N q —The positive pressure between the completion string and casing under the previous operating condition, in Newtons.

[0323]

[0324] Figure 1 This is a flowchart illustrating a method for determining the buckling phenomenon of a tubular column according to an embodiment of this disclosure. See also... Figure 1 The method includes:

[0325] Step S101: Determine the stress and moment of the micro-element of the test column. The stress of the micro-element is the resultant force of gravity, support reaction force, friction force and pressure acting on the micro-element. The moment of the micro-element is the bending moment and torque of the micro-element.

[0326] The test column is composed of multiple micro-elements, which are the smallest units that make up the test column. The temperature, pressure and other parameters can be the same at different points in the same micro-element, which makes it easy to determine the stress and torque of the micro-element.

[0327] As mentioned earlier, the tubing string in an oil well is affected by piston effect, bulging effect, temperature effect, bending effect, and friction effect. These effects can cause deformation of the tubing string, which may lead to buckling. To determine whether buckling has occurred, a stress analysis can be performed on each micro-element of the tubing string to obtain the stress and moment of the micro-element of the tubing string under test.

[0328] Step S102: Determine the equilibrium differential equation of the infinitesimal element based on its stress and torque. The equilibrium differential equation of the infinitesimal element includes the stress equilibrium differential equation and the torque equilibrium differential equation.

[0329] If the test string is in equilibrium downhole, then there must be a state of force equilibrium, meaning the sum of the stress vectors of the infinitesimal elements and the resultant torque of the infinitesimal elements are both zero. Adding the vector sums of the gravity, support reactions, friction, and pressure of the infinitesimal elements and setting the sum to zero yields the stress equilibrium differential equation for the infinitesimal elements. Then, adding the torques of the infinitesimal elements and setting the sum to zero yields the torque equilibrium differential equation for the infinitesimal elements.

[0330] Step S103: Determine the buckling differential equation of the micro-element based on the equilibrium equation of the micro-element. The buckling differential equation of the micro-element represents the total force and total deformation of each micro-element of the test column.

[0331] By iterating over the stress equilibrium differential equation and the moment equilibrium differential equation of the infinitesimal element, the buckling differential equation of the infinitesimal element is obtained. The buckling differential equation of the infinitesimal element represents the relationship between the stress and moment of the infinitesimal element and the intrinsic parameters of the infinitesimal element (e.g., Young's modulus of elasticity, temperature, pressure of the material).

[0332] Step S104: Determine whether the test column has buckled based on the buckling differential equation of the infinitesimal element.

[0333] After obtaining the buckling differential equation of the infinitesimal element, the intrinsic parameters of each infinitesimal element are substituted into the buckling differential equation to obtain the total force and total deformation of each infinitesimal element. Then, the force and deformation of each infinitesimal element of the test column are used to determine whether buckling has occurred in the test column.

[0334] In this embodiment, by performing individual stress and strain analysis on each micro-element of the test string, a buckling differential equation for each micro-element is established. Then, based on the buckling differential equation, the total force and total deformation of each micro-element are determined, thereby determining whether buckling has occurred in the test string. This method can determine whether buckling has occurred in the downhole test string. If buckling has occurred, the operators can then straighten the downhole string based on the force and deformation, preventing damage to the tubing and affecting normal oilfield production.

[0335] Figure 2 This is a flowchart illustrating a method for determining the buckling phenomenon of a tubular column according to an embodiment of this disclosure. See also... Figure 2 The method includes:

[0336] Step S201: Determine the gravity, support reaction force, friction force, and pressure of each micro-element of the test column.

[0337] Since the stress of a micro-element includes components in three directions within the body coordinate system, determining the stress of a micro-element requires expressing the components of the stress in the three directions within the body coordinate system separately.

[0338] The stresses acting on the infinitesimal element can be expressed as follows:

[0339] 1. Gravity of infinitesimal elements:

[0340] G = qe k (49)

[0341] In formula (49):

[0342] e k —A vector direction of natural coordinates.

[0343] In theoretical mechanics, the acceleration vector of a particle moving along a curve is often decomposed into two components: the tangent and the normal along the track. If the tangent and the normal of the track are also considered as a coordinate system, this coordinate system is called the natural coordinate system.

[0344] 2. Support reaction force between the infinitesimal element and the inner wall of the casing:

[0345]

[0346] In formula (50),

[0347] e r —A vector direction of natural coordinates.

[0348] 3. The frictional force of a micro-element includes the viscous frictional resistance of the fluid flow on the inner wall of the micro-element, the viscous frictional resistance of the fluid flow on the outer wall of the micro-element, the axial frictional force between the completion string and the inner wall of the casing, and the circumferential frictional force between the completion string and the inner wall of the casing.

[0349] Viscous frictional resistance of fluid flow on the inner wall of a micro-element:

[0350] f fi =±S i τ fi e1 (51)

[0351] In formula (51),

[0352] S i —Circumference of the inner wall of the completion string, in meters;

[0353] τ ft—Viscous shear stress between the fluid and the inner wall of the completion string, in Newtons per square meter.

[0354] Viscous frictional resistance of fluid flow on the outer wall of the micro-element:

[0355] f fo =±S o τ fo e1 (52)

[0356] In formula (52),

[0357] S o —Perimeter of the outer wall of the completion string, in meters;

[0358] τ fo —Viscous shear stress between the fluid and the outer wall of the completion string, in Newtons per square meter.

[0359] Axial friction between the micro-element and the inner wall of the casing:

[0360] f fz =±f kl Ne1 (53)

[0361] In formula (53),

[0362] f kl — The axial coulombic friction coefficient between the completion string and the inner wall of the casing.

[0363] Circumferential friction between the micro-element and the inner wall of the casing:

[0364] f fh =±f hx N(sinβe2+cosβe3) (54)

[0365] In formula (54),

[0366] f hx — The coefficient of circumferential friction between the completion string and the inner wall of the casing.

[0367] 4. The pressure acting on the micro-element, which is the fluid pressure exerted by the downhole fluid on the micro-element.

[0368] The fluid pressure on the micro-element from the test column can be decomposed into the following three forces: the first axial compressive load P acting on section s. i (s)A i The second axial compressive load P acting on the s+ds section i (s+ds)A i First distributed load F fbi First distributed load F fbi It can be represented as:

[0369]

[0370] In formula (55),

[0371] P i —Internal pressure, unit: megapascal;

[0372] S et —Natural coordinate system e t Displacement in direction, unit: meters:

[0373] S en —Natural coordinate system e n Displacement in direction, unit: meters:

[0374] S eb —Natural coordinate system e b Displacement in direction, unit: meters.

[0375] Among them, e t Direction, e n Direction and e b The directions are mutually perpendicular.

[0376]

[0377] In formula (56),

[0378] α—Well inclination angle, unit: degrees.

[0379]

[0380]

[0381] Then the first distributed load F fbi It can be represented as:

[0382]

[0383] The fluid pressure on the micro-element from outside the test column can be decomposed into the following three forces: the third axial compressive load P acting on section s. o (s)A o The axial fourth compressive load P acting on the s+ds section o (s+ds)A o The second distributed load Ffbo can be expressed as:

[0384]

[0385] In formula (60),

[0386] P o —Axial pressure, unit: Newton;

[0387] φ—azimuth angle, i.e., τ A The projection τ′ on the Oxy plane A The angle between the coordinate system and the x-coordinate system, in degrees.

[0388] Step S202: Decompose each of gravity, support reaction force, friction force and pressure into components in three directions within the body coordinate system.

[0389] In step S201, the gravity, support reaction force, friction force, and pressure acting on the infinitesimal element have been determined. To facilitate the establishment of the force equilibrium equations for the infinitesimal element, the stresses acting on each infinitesimal element are decomposed in the body coordinate system:

[0390] Gravity is decomposed according to the following formula (61):

[0391] G = q τ e τ +q n e n +q b e b (61)

[0392] In formula (61):

[0393] G—gravity, unit: Newton;

[0394] e τ —A direction vector within natural coordinates;

[0395] q τ —Gravity in e τ The component in the direction in which it is located, in Newtons;

[0396] e n —A direction vector within natural coordinates;

[0397] q n —Gravity in e n The component in the direction in which it is located, in Newtons;

[0398] e b —A direction vector within natural coordinates;

[0399] q b —Gravity in e b The component in the direction in which it is located, in Newtons.

[0400] Among them, e τ The direction, e n The direction and e b The directions they are in are perpendicular to each other.

[0401] The support reaction force is decomposed according to the following formula (62):

[0402] N=Ncosβe2+Nsinβe3 (62)

[0403] In formula (62),

[0404] —A reaction force, unit: Newton;

[0405] N—the component of the support reaction force in one direction of the natural coordinate system, in Newtons;

[0406] β—Coefficient of thermal expansion of the material of the test column, in meters per degree Celsius;

[0407] e2—a direction vector of natural coordinates;

[0408] e3—A direction vector of natural coordinates.

[0409] Frictional force includes Coulomb friction and viscous friction. Coulomb friction is the sum of the axial friction between the infinitesimal element and the inner wall of the casing and the circumferential friction between the infinitesimal element and the inner wall of the casing. Coulomb friction is decomposed according to the following formula (63):

[0410] f kl =±f kl Ne1±f hx Nsinβe2±f hx Ncosβe3 (63)

[0411] In formula (63),

[0412] f kl — Coulomb friction, unit: Newton;

[0413] e1—a direction vector of natural coordinates;

[0414] f hx —The circumferential friction coefficient between the test string and the inner wall of the casing.

[0415] Viscous friction is the sum of the viscous frictional resistance of the fluid flow on the inner wall of the micro-element and the viscous frictional resistance of the fluid flow on the outer wall of the micro-element. Viscous friction is decomposed according to the following formula (64):

[0416] f nz =±(S) i τ fi +S o τ fo )e1 (64)

[0417] In formula (64),

[0418] fhz —Viscous friction, unit: Newton;

[0419] S i —Circumference of the inner wall of the section of the pipe to be tested, in meters;

[0420] τ fi —Viscous shear stress between the fluid and the inner wall of the test tube, in Newtons per square meter;

[0421] S o —Circumference of the outer wall of the section of the pipe to be tested, in meters;

[0422] τ fo —The viscous shear stress between the fluid and the outer wall of the test tube, in Newtons per square meter.

[0423] Pressure includes the first distributed load F fbi Second distributed load F fbo The sum of these equations yields the pressure F according to formulas (59) and (60). fb :

[0424]

[0425] The pressure is decomposed in the body coordinate system according to the following formula (66):

[0426] F fb =[P2][e1,e2,e3] T (66)

[0427] in:

[0428]

[0429] The final result is:

[0430] F fb =(Ffbi τ -Ffbo τ )e τ +(Ffbi n -Ffbo n )e n +(Ffbi b -Ffbo b )e b (68)

[0431] In formula (68),

[0432] F fb —Pressure, unit: Newton;

[0433] Ffbi τ —The first distributed load of pressure in e τComponent in direction, unit: Newton;

[0434] Ffbo τ —The second distributed load of pressure in e τ Component in direction, unit: Newton;

[0435] Ffbi n —The first distributed load of pressure in e n Component in direction, unit: Newton;

[0436] Ffbo n —The second distributed load of pressure in e n Component in direction, unit: Newton;

[0437] Ffbi b —The first distributed load of pressure in e b Component in direction, unit: Newton;

[0438] Ffbo b —The second distributed load of pressure in e b Component in direction, unit: Newton.

[0439] Step S203: Combine the components of gravity, support reaction, friction and pressure in each direction to obtain the stress components of the infinitesimal element in the three directions within the body coordinate system.

[0440] The stresses of the infinitesimal element in the three directions of the body coordinate system are combined and then expressed as F. w1 F w2 and F w3 To represent the stresses in the directions e1, e2, and e3, we can obtain:

[0441]

[0442] In formula (69),

[0443] F w1 —The component of the stress on the infinitesimal element in the direction of e1, in Newtons;

[0444] F w2 —The component of the stress on the infinitesimal element in the direction of e2, in Newtons;

[0445] F w3 —The component of the stress on the infinitesimal element in the direction of e3, in Newtons.

[0446] Therefore, stress in the body coordinate system can be expressed as:

[0447] F w =F w1 e1+Fw2 e2+F w3 e3 (70)

[0448] In the formula: F w —Stress experienced by a infinitesimal element, in Newtons.

[0449] Step S204: Determine the equilibrium differential equation of the infinitesimal element based on its stress and torque. The equilibrium differential equation of the infinitesimal element includes the stress equilibrium differential equation and the torque equilibrium differential equation.

[0450] The infinitesimal element is in equilibrium under stress, and the equilibrium equation can be expressed as:

[0451]

[0452] In formula (71):

[0453] —The resultant force in three directions, unit: Newton;

[0454] —The resultant torque in three directions, in Newton-meters.

[0455] The stress and torque acting on the infinitesimal element can be expressed in a three-dimensional coordinate system as follows:

[0456]

[0457]

[0458]

[0459]

[0460] Substituting the gravity, support reaction, friction, and pressure of the infinitesimal element into formula (71), we obtain the stress equilibrium differential equation of the infinitesimal element as follows:

[0461]

[0462] In formula (76),

[0463] F1—Axial stress, unit: Newton;

[0464] F2 — Shear force in natural coordinates e2, unit: Newton;

[0465] F3—Shear force in the direction of natural coordinate e3, unit: Newton;

[0466] k n —A component of borehole curvature in natural coordinates, in degrees per meter;

[0467] k b —A component of borehole curvature in natural coordinates, in degrees per meter;

[0468] k t —A component of borehole curvature in natural coordinates, in degrees per meter.

[0469] The torque equilibrium differential equation of the infinitesimal element is:

[0470]

[0471] In formula (77),

[0472] M1 — Torque in natural coordinates e1, unit: Newton-meter;

[0473] M2 — Torque in natural coordinates e2, unit: Newton-meter;

[0474] M3 — Torque in natural coordinates e3, unit: Newton-meter.

[0475] Step S205: Determine the strain of the infinitesimal element based on the stress-strain relationship and the stress within the element. The material of the test column is isotropic, and the stress and strain exhibit the following constitutive relationship:

[0476]

[0477] In formula (78):

[0478] E—Young's modulus of elasticity of the tubular material to be tested, in Pascals;

[0479] G—Shear modulus of elasticity of the tubular material to be tested, unit: Pascal;

[0480] A—Cross-sectional area of ​​the test tube, unit: square meters;

[0481] A n —in e n Shear area in the direction of the shear line, unit: square meters;

[0482] A b —in e b Shear area in the direction of the shear line, unit: square meters;

[0483] ε τ —in natural coordinates e τ Strain in direction;

[0484] ε n —in natural coordinates e n Strain in direction;

[0485] ε b —in natural coordinates e b Strain in direction.

[0486] Then calculate the strain:

[0487]

[0488] In formula (79):

[0489] u τ — Angular components at θ τ Linear displacement on;

[0490] u n — Angular components at θ n Linear displacement on;

[0491] u b — Angular components at θ b Linear displacement on;

[0492] k — Change in curvature, in degrees;

[0493] θ τ — Angular component in the τ direction, in degrees;

[0494] θ n — Angular component in the n-direction, in degrees;

[0495] θ b — Angular component in the direction of b, in degrees;

[0496] T—Deflection, unit: degrees.

[0497] Step S206: Determine the curvature change of the infinitesimal element based on the relationship between torque and curvature change and the torque of the infinitesimal element.

[0498] The test string is a cylinder, and every point on the string has curvature. When the string twists, every point on the string will have deflection. Using the wellhead O point as the origin of the coordinate system, an O... xyz A right-handed rectangular coordinate system, using vector e respectively. i e j e k Let r(s) represent the unit vector along the x, y, z directions of the coordinate system. The position vector of any point A(x, y, z) on the wellbore axis in three-dimensional space can be represented as a function of arc length:

[0499] r A (s)=x A (s A )e i +y A (s A )e j +z A (s A )ek (80)

[0500] The position increment corresponding to point A can be expressed as:

[0501] dr A =dx A e i +dy A e j +dz A e k (81)

[0502] In equations (80) and (81):

[0503] τ A ds=dr A (82)

[0504]

[0505]

[0506]

[0507] τ A =sinαcosφe i +sinαsinφe j +cosαe k (86)

[0508] in:

[0509] τ A —A unit vector pointing from point A toward the tangent to the wellbore trajectory;

[0510] α—τ A The angle between the coordinate system z and the inclination angle, in degrees;

[0511] φ—τ A The projection τ on the Oxy plane A The angle between the azimuth and the x-coordinate system, i.e., the azimuth angle, in degrees;

[0512] s—Wellbore arc length, unit: meters.

[0513] The curvature κ of the wellbore trajectory curve A and torsion T A It can be calculated using equations (87) and (88):

[0514]

[0515]

[0516] For a beam structure with a circular cross-section, the following constitutive relationship exists between the moment and the change in curvature:

[0517]

[0518] In formula (89),

[0519] M1—Torque in the direction of natural coordinate e1, unit: Newton-meter;

[0520] M2—Torque in the direction of natural coordinate e2, unit: Newton-meter;

[0521] M3—Torque in the direction of natural coordinate e3, unit: Newton-meter;

[0522] J—Polar moment of inertia of the cross section of the test tube, unit: Newton-meter;

[0523] I—Moment of inertia of the section of the test tube about the neutral axis of the section, in Newton-meter;

[0524] κ τ —Natural coordinates e τ Change in curvature in direction, in degrees;

[0525] κ n —Natural coordinates e n Change in curvature in direction, in degrees;

[0526] κ b —Natural coordinates e b The change in curvature in a direction, measured in degrees.

[0527] Find the change in curvature:

[0528]

[0529] When the test string buckles inside the well, since the torque at the upper end is not considered, then u τ ≈0, θ τ ≈0, and at the same time, because the sleeve constraint space is very small relative to the rod length, u n u b θ n and θ b Since both are small quantities, we can conclude that:

[0530]

[0531]

[0532] Step S207: Substitute the strain of the infinitesimal element into the stress equilibrium equation of the infinitesimal element to obtain the stress buckling differential equation of the infinitesimal element.

[0533] Step S208: Substitute the curvature change of the infinitesimal element into the torque balance equation to obtain the torque buckling differential equation of the infinitesimal element.

[0534] Substituting the change in curvature of the infinitesimal element into the torque balance equation, we obtain the first equation:

[0535]

[0536] Differentiating the first equation yields the relationship between the torque of the infinitesimal element and the change in curvature and elastic modulus of the infinitesimal element. This relationship is the torque buckling differential equation of the infinitesimal element.

[0537] Differentiating equation (93) with respect to s, we get:

[0538] F′ w2 =-EI(κ″) b +κ τ κ′ n )+M1κ′ n (94)

[0539] F′ w3 =EI(κ″) n -κ τ κ′ b )+M1κ′ b (95)

[0540] EI(κ″ b +2κ τ κ′ n )-M1κ′ n -F1κ b -F w2 =0 (96)

[0541] EI(κ″ n -2κ τ κ′ b )+M1κ′ b -F1κ n +F w3 =0 (97)

[0542] get:

[0543]

[0544] in:

[0545]

[0546]

[0547] Taking the first and second derivatives of equation (32) with respect to s, we get:

[0548] κ′ n = r·β″′cosβ - 3r·β″β′sinβ - r·β′ 3 cosβ - 2Tr·β″sinβ - 2Tr·β′ 2 cosβ (101)

[0549] κ″ n = r·β″″cosβ - 4r·β″′β′sinβ - 3r·β″ 2 sinβ - 6r·β″β′ 2 cosβ

[0550] + r·β′ 4 sinβ - 2Tr·β″′sinβ - 6Tr·β″β′cosβ + 2Tr·β′ 3 sinβ (102)

[0551] κ′ b = r·β″′sinβ + 3r·β″β′cosβ - r·β′ 3 sinβ + 2T·r·β″cosβ - 2T·r·β′ 2 sinβ (103)

[0552] κ″ b = r·β″″sinβ + 3r·β″ 2 cosβ + 4r·β′β″′cosβ - 6r·β′ 2 β″sinβ

[0553] - r·β′ 4 cosβ + 2T·r·β″′cosβ - 6T·r·β′β″sinβ - 2T·r·β′ 3 cosβ (104)

[0554] Rearranging equations (98) to (104) gives:

[0555] EI[r·β″″sinβ + 3r·β″ 2 cosβ + 4r·β′β″′cosβ - 6r·β′ 2 β″sinβ

[0556] - r·β′ 4 cosβ + 2T·r·β″′cosβ - 6T·r·β′β″sinβ - 2T·r·β′ 3 cosβ + 2κ τ ·

[0557] (r·β″′cosβ - 3r·β″β′sinβ - r·β′ 3cosβ - 2Tr·β″sinβ - 2Tr·β′ 2 cosβ)]

[0558] -M1(r·β″′cosβ - 3r·β″β′sinβ - r·β′ 3 cosβ - 2Tr·β″sinβ

[0559] -2Tr·β′ 2 cosβ) - F1(r·β″sinβ + r·β′ 2 cosβ + 2T·r·β′cosβ + κ)

[0560] =F f2 +ξ3β′sinβ + Ncosβ + ξ4sinβ (105)

[0561] EI[r·β″″cosβ - 4r·β″′β′sinβ - 3r·β″ 2 sinβ - 6r·β″β′ 2 cosβ

[0562] +r·β′ 4 sinβ - 2Tr·β″′sinβ - 6Tr·β″β′cosβ + 2Tr·β′ 3 sinβ - 2κ τ ·

[0563] (r·β″′sinβ + 3r·β″β′cosβ - r·β ′3 sinβ + 2T·r·β″cosβ - 2Tr·β ′2 sinβ)]

[0564] +M1(r·β″′sinβ + 3r·β″β′cosβ - r·β ′3 sinβ + 2T·r·β″cosβ

[0565] -2T·r·β ′2 sinβ) - F1(r·β″cosβ - r·β ′2 sinβ - 2Tr·β′sinβ)

[0566] +F f3 -ξ3β′cosβ + Nsinβ - ξ4cosβ = 0 (106)

[0567] Equation (106) can be arranged as:

[0568] cosβ{EI[3β″<000043​​​​+2κ τ (β″′ - β′ 3 -2Tβ′ 2 )]

[0569] -M1(β″′ - β′ 3 -2Tβ′ 2 ) - F1(β′ 2 +2T·β′) - N / d}+sinβ{EI[β″″ - 6β′ 2 β″

[0570] -6Tβ′β″ + 2κ τ (-3β″β′ - 2Tβ″)] - M1(-3β″β′ - 2Tβ″) - F1β″ - ξ3β′ / r

[0571] -ξ4 / r} - F1κ / r - F f2 / r=0 (107)sinβ{EI[β′ 4 -4β″′β′ - 3β″ 2 -2Tβ″′ + 2Tβ′ 3 -2κ τ (β″′ - β′ 3 -2Tβ′ 2 )]

[0572] +M1(β″′ - β′ 3 -2Tβ′ 2 ) + F1(β′ 2 +2Tβ′) + N / d}+cosβ{EI[β″″ - 6β″β′ 2

[0573] -6Tβ″β′ - 2κ τ (+3β″β′ + 2Tβ″)] + M1(3β″β′ + 2Tβ″) - F1β″ - ξ3β′ / r

[0574] -ξ4 / r} + F f3 / r=0 (108) Multiply Equation (107) by sinβ + Equation (108) by cosβ, we get:

[0575] EI[β″″ - 6β′ 2 β″ - 6Tβ″β′ - 2κ τ (+3β″β′ + 2Tβ″)] + M1(3β″β′ + 2Tβ″) - F1β″

[0576] -ξ3β′ / d - ξ4 / r + cosβF f3 / r - sinβF1κ / r - sinβF f2 / r=0 (109) Subtracting equation (107)×cosβ from equation (108)×sinβ, we get:

[0577] {EI[3β″ 2 +4β′β″′-β′ 4 +2Tβ″′-2Tβ′ 3 +2κ τ (β″′-β′ 3 -2Tβ′ 2 )]-M1(β″′

[0578] -β′ 3 -2Tβ′ 2 )-F1(β′ 2 +2T·β′)-N / r}-cosβF1κ / r

[0579] -cosβF f2 / r-sinβF f3 / r=0 (110) Rearranging equation (110), we get:

[0580] N=EIr[3β″ 2 +4β′β″′-β′ 4 +2Tβ″′-2Tβ′ 3 +2κ τ (β″′-β′ 3 -2Tβ′ 2 )]

[0581] -M1r(β″′-β′ 3 -2Tβ′ 2 )-F1r(β′ 2 +2T·β′)}-cosβF1κ

[0582] -cosβF f2 -sinβF f3 (111) For isotropic completion string materials, the following relationship exists:

[0583] E=2G(1+ν) (112)

[0584] In the formula: ν—Poisson's ratio of the material.

[0585] Since the completion string has a circular cross-section, J = 2I. From equations (110) and (111), the buckling equation of the three-dimensional directional well completion string can be obtained as follows:

[0586] EIr(β″″-6β′ 2 β″-6Tβ″β′)-M1r(1+2ν)(3β″β′+2Tβ″)-F1rβ″

[0587] -ξ4+cosβF f3 -sinβF1κ-sinβF f2 =0 (113)

[0588] N=EIr[3β″ 2 +4β′β″′-β′ 4 +2Tβ″′-2Tβ′ 3 ]+M1(1+2ν)r(β″′-β′ 3

[0589] -2Tβ′ 2 )-F1r(β′ 2 +2T·β′)-cosβF1κ-cosβF f2 -sinβF f3 (114)

[0590] The total bending moment on the cross-section of the completion string can be expressed as:

[0591]

[0592] Equations (113) to (115) are the buckling differential equations of the three-dimensional directional well completion string, which are comprehensive mechanical equations describing the buckling deformation and load distribution of the completion string in a three-dimensional curved wellbore.

[0593] Step S209: Based on the buckling differential equation of the micro-element, determine the total force and total deformation of each micro-element of the test column.

[0594] From the buckling differential equation of the infinitesimal element, we know that the buckling differential equation of the infinitesimal element and the inherent parameters of the infinitesimal element, the moment of inertia of the section of the pipe under test about the neutral axis of the section, etc., are all present. By substituting the inherent parameters of the infinitesimal element into the buckling differential equation of the infinitesimal element, we can determine the total force and total deformation of each infinitesimal element of the pipe under test.

[0595] Step S210: Determine whether the test column has buckled based on the total force and total deformation of each micro-element.

[0596] For example, after determining the stress and strain of each micro-element, a model diagram of the stress and deformation of each micro-element of the test column can be simulated on computer software, and the buckling state of the column in the model diagram can be used to determine whether the test column has buckled.

[0597] In this embodiment of the disclosure, the type of buckling phenomenon occurring in the tubing can be determined according to Table 1:

[0598] Table 1

[0599]

[0600] For example, if the buckling of the column in the model diagram exceeds the threshold, it indicates that the column has buckled.

[0601] The method for determining the buckling phenomenon of the completion string provided in this disclosure starts from the position of the completion string in the three-dimensional wellbore and systematically considers the safety requirements of the completion string under piston effect, bulging effect, temperature effect, bending effect, and friction effect to determine the buckling morphology of the completion string. This method is suitable for the characteristics of ultra-deep wells, is scientific, comprehensive, and accurate, and solves the problem of accurately describing the buckling behavior of completion strings in ultra-deep gas wells. It provides a basis for buckling management of completion strings in ultra-deep gas wells and is very convenient for field operation.

[0602] The method for determining the buckling phenomenon of the tubing string provided in this embodiment is applied to a certain well. In the mechanical environment of a certain ultra-deep, high-temperature, and high-production well, the tubing string inevitably bears a more complex mechanical environment. This section uses the on-site tubing string dimensions as an example for calculation. The structure of the tubing string is shown in Table 2. The working environment under hot production conditions is as follows: packer position: 7300 mm; casing inner diameter: 152.5 mm; annular protection fluid density: 1.0 g / cm³; production: 2 million cubic meters / day; oil pressure: 50 MPa; wellhead temperature: 145 degrees Celsius; bottom hole temperature: 180 degrees Celsius.

[0603] Table 2

[0604]

[0605] In this embodiment, the buckling phenomenon of the tubing is shown in the figure below. Figure 3 and Figure 4 As shown.

[0606] Figure 3 This is a diagram showing the buckling phenomenon of a tubular column in the X direction, provided in an embodiment of this disclosure. Figure 4 This is a diagram illustrating the buckling phenomenon of a tubular column in the Y direction, as provided in an embodiment of this disclosure. See also... Figure 3 and Figure 4 The greater the depth of the tubing, the better.

[0607] Description of buckling behavior of completion tubing in ultra-deep gas wells obtained using the methods of embodiments of this disclosure.

[0608] 1) Determination of the forces on the tubing string in a three-dimensional wellbore: Based on the wellbore coordinate system and the forces on the tubing string micro-element, the constitutive relationship of the tubing string is summarized, and then the buckling differential equation of the tubing string is established; then the buckling differential equation of the tubing string is solved according to the differential quadrature method and the set boundary conditions.

[0609] 2) Determination of various effects and forces during production: Considering the piston effect, bulging effect, temperature effect, bending effect, and friction effect, the total deformation and total force caused by these effects on the completion string are combined, and the curve of the buckling displacement of the completion string as a function of well depth is plotted to form a chart.

[0610] The embodiments disclosed herein systematically consider the safety requirements of completion strings for ultra-deep gas wells. Based on the actual well conditions and operating conditions of ultra-deep gas wells, the buckling morphology of the completion string is calculated and described, which has better pertinence and reliability, and can better guide the buckling prevention of completion strings for ultra-deep gas wells.

[0611] Figure 5 This is a schematic diagram of a device for determining the buckling phenomenon of a tubular column according to an embodiment of this disclosure. See also... Figure 5 The device includes: a first determining module 301, a second determining module 302, a third determining module 303, and a fourth determining module 304.

[0612] The first determining module 301 is configured to determine the stress and torque of the micro-element of the test column. The stress of the micro-element is the resultant force of gravity, support reaction force, friction force and pressure acting on the micro-element, and the torque of the micro-element is the bending moment and torque of the micro-element.

[0613] The second determining module 302 is configured to determine the equilibrium differential equation of the infinitesimal element based on the stress and torque of the infinitesimal element. The equilibrium differential equation of the infinitesimal element includes the stress equilibrium differential equation and the torque equilibrium differential equation of the infinitesimal element.

[0614] The third determining module 303 is configured to determine the buckling differential equation of the micro-element based on the equilibrium equation of the micro-element. The buckling differential equation of the micro-element represents the total force and total deformation of each micro-element of the test column.

[0615] The fourth determination module 304 is configured to determine whether the test column has buckled based on the buckling differential equation of the infinitesimal element.

[0616] The stress of the infinitesimal element includes components in three directions within the body coordinate system. The first determining module 301 is configured as follows:

[0617] The gravity, support reaction force, friction force, and pressure acting on each micro-element of the test column are determined separately. Each of the gravity, support reaction force, friction force, and pressure is decomposed into components in three directions within the body coordinate system. The components of gravity, support reaction force, friction force, and pressure in each direction of the micro-element are combined to obtain the stress components of each micro-element in the three directions within the body coordinate system.

[0618] The first determining module 301 is configured to decompose gravity, support reaction force, friction force, and pressure according to the following formulas:

[0619] Decompose gravity according to the following formula:

[0620] G = q τ e τ +qn e n +q b e b

[0621] in:

[0622] G—gravity, unit: Newton;

[0623] e τ —A direction vector within natural coordinates;

[0624] q τ —Gravity in e τ The component in the direction in which it is located, in Newtons;

[0625] e n —A direction vector within natural coordinates;

[0626] q n —Gravity in e n The component in the direction in which it is located, in Newtons;

[0627] e b —A direction vector within natural coordinates;

[0628] q b —Gravity in e b The component in the direction in which it is located, in Newtons;

[0629] The support reactions can be decomposed according to the following formula:

[0630]

[0631] in,

[0632] —A reaction force, unit: Newton;

[0633] N—the component of the support reaction force in one direction of the natural coordinate system, in Newtons;

[0634] β—Coefficient of thermal expansion of the material of the test column, in meters per degree Celsius;

[0635] e2—a direction vector of natural coordinates;

[0636] e3—a direction vector of natural coordinates;

[0637] Frictional force includes Coulomb friction and viscous friction. Coulomb friction can be decomposed according to the following formula:

[0638] f kl =±f kl Ne1±f hx Nsinβe2±f hxNcosβe3

[0639] in,

[0640] f kl — Coulomb friction, unit: Newton;

[0641] e1—a direction vector of natural coordinates;

[0642] f hx —The coefficient of circumferential friction between the test tubing and the inner wall of the casing;

[0643] The viscous friction reaction force is decomposed according to the following formula:

[0644] f nz =±(S) i τ fi +S o τ fo )e1

[0645] in,

[0646] f nz —Viscous friction, unit: Newton;

[0647] S i —Circumference of the inner wall of the section of the pipe to be tested, in meters;

[0648] τ fi —Viscous shear stress between the fluid and the inner wall of the test tube, in Newtons per square meter;

[0649] S o —Circumference of the outer wall of the section of the pipe to be tested, in meters;

[0650] τ fo —Viscous shear stress between the fluid and the outer wall of the test tubing, in Newtons per square meter; The pressure support reaction force is decomposed according to the following formula:

[0651] F fb =(Ffbi, -Ffbo) τ )e τ 10 (Ffbi) n -Ffbo n )e n 10 (Ffbi) b -Ffbo b )e b

[0652] in,

[0653] F fb —Pressure, unit: Newton;

[0654] Ffbi τ—The first distributed load of pressure in e τ Component in direction, unit: Newton;

[0655] Ffbo τ —The second distributed load of pressure in e τ Component in direction, unit: Newton;

[0656] Ffbi n —The first distributed load of pressure in e n Component in direction, unit: Newton;

[0657] Ffbo n —The second distributed load of pressure in e n Component in direction, unit: Newton;

[0658] Ffbi b —The first distributed load of pressure in e b Component in direction, unit: Newton;

[0659] Ffbo b —The second distributed load of pressure in e b Component in direction, unit: Newton.

[0660] The second determining module 302 is configured to determine the stress equilibrium differential equation of the infinitesimal element as follows:

[0661]

[0662] in,

[0663] F1—Axial force, unit: Newton;

[0664] F2—Shear force in the direction of natural coordinate e2, unit: Newton;

[0665] F3—Shear force in the direction of natural coordinate e3, unit: Newton;

[0666] F w1 —Stress in the natural coordinate e1 direction, in Newtons;

[0667] F w2 —Stress in the natural coordinate e2 direction, in Newtons;

[0668] F w3 —Stress in the natural coordinate e3 direction, in Newtons;

[0669] k κ —Natural coordinates e τ Change in curvature in the direction;

[0670] k n —Natural coordinates en The change in curvature in the direction;

[0671] k b —Natural coordinates e b The change in curvature in the direction.

[0672] The torque equilibrium differential equation for the infinitesimal element is determined as follows:

[0673]

[0674] in,

[0675] M1—Torque in the direction of natural coordinate e1, unit: Newton-meter;

[0676] M2—Torque in the direction of natural coordinate e2, unit: Newton-meter;

[0677] M3 — Torque in the direction of natural coordinate e3, unit: Newton-meter.

[0678] The third determining module 303 is configured to: determine the strain of the micro-element based on the relationship between stress and strain and the stress of the micro-element; determine the curvature change of the micro-element based on the relationship between torque and curvature change and the torque of the micro-element; substitute the strain of the micro-element into the stress equilibrium equation of the micro-element to obtain the stress buckling differential equation of the micro-element; and substitute the curvature change of the micro-element into the torque equilibrium equation to obtain the torque buckling differential equation of the micro-element.

[0679] The third determining module 303 is configured to: substitute the curvature change of the infinitesimal element into the torque balance equation to obtain the first equation; differentiate the first equation to obtain the relationship between the torque of the infinitesimal element and the curvature change and elastic modulus of the infinitesimal element, which is the torque buckling differential equation of the infinitesimal element.

[0680] The fourth determination module 304 is configured to: determine the total force and total deformation of each micro-element of the test column based on the buckling differential equation of the micro-element; and determine whether the test column has buckled based on the total force and total deformation of each micro-element.

[0681] This disclosure also provides an electronic device that may include a processor and a memory, the memory storing at least one line of program code that is loaded and executed by the processor to implement the aforementioned method.

[0682] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this disclosure. See also... Figure 6The electronic device 400 includes a central processing unit (CPU) 401, a system memory 404 including random access memory (RAM) 402 and read-only memory (ROM) 403, and a system bus 405 connecting the system memory 404 and the CPU 401. The electronic device 400 also includes a basic input / output system (I / O system) 406 that facilitates information transfer between various devices within the computer, and a mass storage device 407 for storing the operating system 413, application programs 414, and other program modules 415.

[0683] The basic input / output system 406 includes a display 408 for displaying information and an input device 409 for user input, such as a mouse or keyboard. Both the display 408 and the input device 409 are connected to the central processing unit 401 via an input / output controller 410 connected to the system bus 405. The basic input / output system 406 may also include the input / output controller 410 for receiving and processing input from multiple other devices such as a keyboard, mouse, or electronic stylus. Similarly, the input / output controller 410 also provides output to a display screen, printer, or other types of output devices.

[0684] Mass storage device 407 is connected to central processing unit 401 via a mass storage controller (not shown) connected to system bus 405. Mass storage device 407 and its associated computer-readable media provide non-volatile storage for electronic device 400. That is, mass storage device 407 may include computer-readable media (not shown) such as hard disk or CD-ROM drive.

[0685] Without loss of generality, computer-readable media can include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer storage media include RAM, ROM, erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other solid-state storage technologies, compact disc read-only memory (CD-ROM), digital video disc (DVD) or other optical storage, magnetic tape cassettes, magnetic tape, disk storage, or other magnetic storage devices. Of course, those skilled in the art will recognize that computer storage media are not limited to the above-mentioned types. The system memory 404 and mass storage device 407 described above can be collectively referred to as memory.

[0686] According to various embodiments of this disclosure, electronic device 400 can also be connected to a remote computer on a network, such as the Internet. That is, electronic device 400 can be connected to network 412 via network interface unit 411 connected to system bus 405, or it can use network interface unit 411 to connect to other types of networks or remote computer systems (not shown).

[0687] The aforementioned memory also includes one or more programs, which are stored in the memory and configured to be executed by the CPU. The CPU 401 implements the aforementioned method for determining the buckling phenomenon of the tubing by executing the one or more programs.

[0688] Those skilled in the art will understand that Figure 6 The structure shown does not constitute a limitation on the electronic device 400, and may include more or fewer components than shown, or combine certain components, or use different component arrangements.

[0689] This disclosure also provides a computer-readable storage medium storing at least one line of program code, which is loaded and executed by the processor to implement the method described above. For example, the computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, or optical data storage device.

[0690] This disclosure also provides a computer program product that stores at least one piece of program code, which is loaded and executed by the processor to implement the method described above.

[0691] It should be understood that "multiple" as used in this article refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0692] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0693] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A method for determining the buckling phenomenon of a tubular column, characterized in that, The method includes: The stress and moment of the micro-element of the test column are determined. The stress of the micro-element is the resultant force of gravity, support reaction force, friction force, and pressure acting on it. The moment of the micro-element is its bending moment and torque. The test column is composed of multiple micro-elements, which are the smallest units that make up the test column. The temperature and pressure are the same at all points within the same micro-element. The test column is deformed by the piston effect, bulging effect, temperature effect, bending effect, and friction effect. The equilibrium differential equation of the infinitesimal element is determined based on the stress and torque of the infinitesimal element. The equilibrium differential equation of the infinitesimal element includes the stress equilibrium differential equation and the torque equilibrium differential equation of the infinitesimal element. The buckling differential equation of the micro-element is determined based on its equilibrium differential equation. The buckling differential equation of the micro-element represents the total force and total deformation of each micro-element of the test column. The buckling differential equation of the micro-element represents the relationship between the stress and moment of the micro-element and the inherent parameters of the micro-element. Based on the buckling differential equation of the micro-element, the total force and total deformation of each micro-element of the test column are determined; After determining the total force and total deformation of each of the micro-elements, a model diagram of the force and deformation of each micro-element of the test column is simulated on computer software. Based on the buckling state of the column in the model diagram, it is determined whether the test column has buckled. The stress equilibrium differential equation of the infinitesimal element is: in, F1—Axial force, unit: Newton; F2—Shear force in the direction of natural coordinate e2, unit: Newton; F3—Shear force in the direction of natural coordinate e3, unit: Newton; F w1 —Stress in the natural coordinate e1 direction, in Newtons; F w2 —Stress in the natural coordinate e2 direction, in Newtons; F w3 —Stress in the natural coordinate e3 direction, in Newtons; k τ —Natural coordinates e τ Change in curvature in a direction, unit: negative first meter; k n —Natural coordinates e n Change in curvature in a direction, unit: negative first meter; k b —Natural coordinates e b Change in curvature in a direction, unit: negative first meter; The torque balance differential equation of the infinitesimal element is: in, M1—Torque in the direction of natural coordinate e1, unit: Newton-meter; M2—Torque in the direction of natural coordinate e2, unit: Newton-meter; M3 — Torque in the direction of natural coordinate e3, unit: Newton-meter.

2. The method for determining the buckling phenomenon of the tubular string according to claim 1, characterized in that, The stress of the micro-element includes components in three directions within the body coordinate system. Determining the stress of the micro-element of the test column includes: Determine the gravity, support reaction force, friction force, and pressure acting on each micro-element of the test column; Each of the gravity, the support reaction force, the friction force, and the pressure is decomposed into components in three directions within the body coordinate system; The components of gravity, support reaction force, friction force, and pressure of each micro-element in each direction are combined to obtain the components of stress of each micro-element in the three directions of the body coordinate system.

3. The method for determining the buckling phenomenon of the tubular string according to claim 2, characterized in that, Each of the gravity, the support reaction force, the frictional force, and the pressure is decomposed into components in three directions within the body coordinate system, including: The gravity can be decomposed according to the following formula: G=q τ e τ +q n e n +q b e b in: G—gravity, unit: Newton; e τ —A direction vector within natural coordinates; q τ —Gravity in e τ The component in the direction in which it is located, in Newtons; e n —A direction vector within natural coordinates; q n —Gravity in e n The component in the direction in which it is located, in Newtons; e b —A direction vector within natural coordinates; q b —Gravity in e b The component in the direction in which it is located, in Newtons; The support reaction force can be decomposed according to the following formula: in, —A reaction force, unit: Newton; N—the component of the support reaction force in one direction of the natural coordinate system, in Newtons; β—Coefficient of thermal expansion of the material of the test column, in meters per degree Celsius; e2—a direction vector of natural coordinates; e3—a direction vector of natural coordinates; The frictional force includes Coulomb friction and viscous friction, which can be decomposed according to the following formula: in kl =±f kl Ne1±f hx Nsinβe2±f hx Ncosβe3 in, f kl — Coulomb friction, unit: Newton; e1—a direction vector of natural coordinates; f hx —The coefficient of circumferential friction between the test tubing and the inner wall of the casing; The viscous friction force can be decomposed according to the following formula: f nz =±(S i τ fi +S o τ fo )e1 in, f nz —Viscous friction, unit: Newton; S i —Circumference of the inner wall of the section of the pipe to be tested, in meters; τ fi —Viscous shear stress between the fluid and the inner wall of the test tube, in Newtons per square meter; S o —Circumference of the outer wall of the section of the pipe to be tested, in meters; τ fo —Viscous shear stress between the fluid and the outer wall of the test tube, in Newtons per square meter; The pressure can be decomposed according to the following formula: F fb =(Fby τ -Fbbo τ ) e τ + (Fby n -Fbbo n ) e n + (Fby b -Fbbo b ) e b among them F fb —Pressure, unit: Newton; Ffbi τ —The first distributed load of pressure in e τ Component in direction, unit: Newton; Ffbo τ —The second distributed load of pressure in e τ Component in direction, unit: Newton; Ffbi n —The first distributed load of pressure in e n Component in direction, unit: Newton; Ffbo n —The second distributed load of pressure in e n Component in direction, unit: Newton; Ffbi b —The first distributed load of pressure in e b Component in direction, unit: Newton; Ffbo b —The second distributed load of pressure in e b Component in direction, unit: Newton.

4. The method for determining the buckling phenomenon of the tubular column according to any one of claims 1 to 3, characterized in that, The buckling differential equation of the infinitesimal element includes the stress buckling differential equation and the moment buckling differential equation of the infinitesimal element. The buckling differential equation of the infinitesimal element is determined based on its equilibrium equation, including: The strain of the micro-element is determined based on the relationship between stress and strain and the stress of the micro-element. The curvature change of the infinitesimal element is determined based on the relationship between torque and curvature change and the torque of the infinitesimal element. Substituting the strain of the micro-element into the stress equilibrium equation of the micro-element, we obtain the stress buckling differential equation of the micro-element. Substituting the curvature change of the infinitesimal element into the torque balance equation yields the torque buckling differential equation of the infinitesimal element.

5. The method for determining the buckling phenomenon of the tubular column according to claim 4, characterized in that, Substituting the curvature change of the infinitesimal element into the moment balance equation yields the moment buckling differential equation of the infinitesimal element, including: Substituting the curvature change of the infinitesimal element into the torque balance equation, we obtain the first equation; Differentiating the first equation yields a relationship between the torque of the infinitesimal element and the change in curvature and elastic modulus of the infinitesimal element. This relationship is the torque buckling differential equation of the infinitesimal element.

6. A device for determining the buckling phenomenon of a tubular column, characterized in that, The device includes: The first determining module is configured to determine the stress and torque of the micro-element of the test column. The stress of the micro-element is the resultant force of gravity, support reaction force, friction force, and pressure acting on the micro-element. The torque of the micro-element is the bending moment and torque of the micro-element. The test column is composed of multiple micro-elements, which are the smallest units constituting the test column. The temperature and pressure are the same at all points within the same micro-element. The test column is deformed by the piston effect, bulging effect, temperature effect, bending effect, and friction effect. The second determining module is configured to determine the equilibrium differential equation of the micro-element based on the stress and torque of the micro-element, wherein the equilibrium differential equation of the micro-element includes the stress equilibrium differential equation and the torque equilibrium differential equation of the micro-element. The third determining module is configured to determine the buckling differential equation of the micro-element based on the equilibrium differential equation of the micro-element. The buckling differential equation of the micro-element represents the total force and total deformation of each micro-element of the test column. The buckling differential equation of the micro-element represents the relationship between the stress and moment of the micro-element and the inherent parameters of the micro-element. The fourth determining module is configured to determine the total force and total deformation of each micro-element of the test column based on the buckling differential equation of the micro-element; after determining the total force and total deformation of each micro-element, a model diagram of the force and deformation of each micro-element of the test column is simulated on computer software, and the buckling state of the column in the model diagram is used to determine whether the test column has buckled; The stress equilibrium differential equation of the infinitesimal element is: in, F1—Axial force, unit: Newton; F2—Shear force in the direction of natural coordinate e2, unit: Newton; F3—Shear force in the direction of natural coordinate e3, unit: Newton; F w1 —Stress in the natural coordinate e1 direction, in Newtons; F w2 —Stress in the natural coordinate e2 direction, in Newtons; F w3 —Stress in the natural coordinate e3 direction, in Newtons; k τ —Natural coordinates e τ Change in curvature in a direction, unit: negative first meter; k n —Natural coordinates e n Change in curvature in a direction, unit: negative first meter; k b —Natural coordinates e b Change in curvature in a direction, unit: negative first meter; The torque balance differential equation of the infinitesimal element is: in, M1—Torque in the direction of natural coordinate e1, unit: Newton-meter; M2—Torque in the direction of natural coordinate e2, unit: Newton-meter; M3 — Torque in the direction of natural coordinate e3, unit: Newton-meter.

7. An electronic device, characterized in that, The electronic device includes: processor; Memory used to store processor-executable instructions; The processor is configured to perform the method for determining buckling phenomena of the tubular column according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which is executed by a processor to implement the method for determining the buckling phenomenon of the tubular column as described in any one of claims 1 to 5.

Images