CN106503399B - Peupendicular hole hangs the determination method of tubing string Helical Buckling Critical Load - Google Patents

Abstract

The present invention relates to the determination method that peupendicular hole hangs tubing string Helical Buckling Critical Load, the determination method of this peupendicular hole suspension tubing string Helical Buckling Critical Load includes：Step 1: suspended tubes column parameter is initialized；Step 2: setting up suspension post-buckling equilibrium equation；Step 3: setting up suspension tubing string Helical Buckling analysis method；Step 4: suspension tubing string Helical Buckling is solved；Step 5: the result of calculation post processing of suspension tubing string Helical Buckling；Step 6: suspension tubing string Helical Buckling Critical Load is determined.The present invention considers the influence of suspension tubing string tension segment length and constraint boundary condition, by tubing string length and critical load nondimensionalization, there is provided the universal method for determining peupendicular hole suspension tubing string Helical Buckling Critical Load, not the problem of determination method for solving current tubing string Helical Buckling Critical Load does not account for the influence of the restrained boundary condition and suspension tension section tubing string length of actual suspension tubing string upper and lower ends to Helical Buckling.

Description

Determination method for helical buckling critical load of suspended pipe string in vertical well

technical field

The invention relates to a vertical well suspension pipe string in the technical field of petroleum drilling and production engineering, in particular to a method for determining the helical buckling critical load of a vertical well suspension pipe string.

Background technique

The buckling of tubular strings in the wellbore (such as drill strings, casing strings, test strings, sucker rod strings, coiled tubing, etc.) cracks, plugging, oil recovery, etc.) have serious impacts. The buckling of the drill string will cause the deflection of the drill bit, forming a "dog leg"; the buckling of the tubing will increase the wear of the casing and tubing, and increase the energy consumption. The pipe string is often working in a buckled state. Severe buckling will cause the damage of the pipe string and the locking of the pipe string. key technical issues.

The critical load analysis of vertical well string buckling is one of the important problems. In 1950, Lubinsk first studied the stability of the drill string in the vertical wellbore, derived the bending equation of the drill string in the vertical plane, and gave the series solution of the equation. Under the constraint boundary condition of hinge support at both ends, the beam-column model is adopted, and the dimensionless length is taken as 8, and the critical load calculation method for the buckling of the drill string in the vertical plane is given. Lubinski (1957) and others proposed the concept of spatial helical bending of the pipe string. In 1962, Lubinski first proposed the calculation method of equal-pitch spatial buckling of pipe strings in vertical wells, assuming that the buckling is a spatial helix, and using the energy method to derive the relationship between the pitch and the axial pressure. When he proposed this method, he had already pointed out that the spatial helical buckling configuration of the compression section of the actual pipe string is an unequal helix.

Mitchell (1988) studied helical buckling and proved that Lubinski's helical buckling model is only an approximate result. Mitchell's results show that near the neutral point, the Lubinski pitch-axial pressure relationship is not valid because the tubing string may not be in contact with the wellbore. Kwon (1988) adopted the non-equal pitch assumption to analyze the helical buckling of a vertical pipe string under its own weight. By using the principle of virtual work and solving the generalized fourth-order nonlinear beam equation, the analytical formula for pitch calculation is obtained. Zhang Yanglie (1985) analyzed the space helical buckling problem with heavy drill string, and calculated the calculation formula of unequal pitch by using energy method. Wu Jiang (1992), Gao Guohua (1996), Gao Deli (2006) and other researchers, using theoretical calculations, also obtained different formulas for the helical buckling pitch of vertical wells with heavy strings. Hajianmaleki (2014) used ABAQUS finite element software to calculate the helical buckling of heavy pipe strings in vertical wells.

The helical buckling formulas of pipe strings determined by the above researchers are generally derived based on the assumption of equal or unequal pitches, without considering the influence of constraint boundary conditions. However, in addition to being constrained by the wellbore in the wellbore, the vertical well string also has constraint boundary conditions at the upper and lower ends; moreover, the buckling problem below the neutral point is generally studied at present, and the buckling of the tension section above the neutral point is not considered. Impact. Especially the real and ubiquitous helical buckling problem of suspended pipe string in the wellbore, the upper end is suspended in tension and the lower end is under compression. Since Lubinsk first studied the stability of the drill string in the vertical wellbore in 1950, more than 60 years have passed. Unresolved, restricting the engineering technology application level of oil drilling and production strings. Academician Gao Deli (2015) looked forward to the research method of the helical buckling problem of suspended pipe strings, and proposed the research idea of using the beam-column model for the upper suspension section and the differential equation for the lower continuous contact section. However, where the boundary point between the suspension section and the contact section is, there is a relatively large technical difficulty, and there are no related reports on implementation.

At present, there are the following problems in the determination method of the helical buckling critical load of the pipe string: (1) Although it is recognized that at least one complete helix must be formed for the helical buckling of the pipe string, different researchers have determined that the helical section of the helical buckling of the pipe string is infinite There are obvious differences in class length, for example, Zhang Yanglie (1985) is 4.46, Wu Jiang (1992) is 5.55, Gao Guohua (1996) is 5.816, Gao Deli (2006) is 5.62 and Hajianmaleki (2014) is 5.25. (2) The researchers defined the critical load of the helical buckling of the pipe string according to the self-weight of the length of the contact helical section. This method does not consider the constraint boundary conditions at the upper and lower ends of the actual suspended pipe string and the influence of the length of the suspended pipe string on the helical buckling. Therefore, the determined critical load for the helical buckling of the pipe string is unreasonable.

Contents of the invention

An object of the present invention is to provide a method for determining the helical buckling critical load of a vertical well suspended pipe string, which is used to solve the problem that the current method for determining the helical buckling critical load of a pipe string does not consider the actual The constraint boundary conditions at the upper and lower ends of the suspended pipe string and the influence of the length of the suspended pipe string on helical buckling.

The technical solution adopted by the present invention to solve the technical problem is: the method for determining the helical buckling critical load of the vertical well suspended pipe string:

Step 1. Suspension string parameter initialization:

Using the parameters of the suspended pipe string, according to the density of the pipe string and the density of the liquid inside and outside the pipe string, the load q per unit length of the pipe string is obtained as:

Dimensionless the length of the pipe string, the dimensionless total length ξ _L of the pipe string can be obtained as:

The parameters of the suspended pipe string include pipe string geometric dimension parameters, pipe string material parameters, fluid physical parameters and wellbore inner diameter D _I , wherein geometric parameters include inner diameter Di, outer diameter D _o and length L; pipe string material parameters include string elastic modulus Quantity E and density ρ _s ; fluid physical parameters include liquid density ρ _i inside the pipe string and liquid density ρ _o outside the pipe string annulus.

Step 2: Establish the buckling equilibrium equation of the suspended pipe string:

Using the initialization parameters of the suspended pipe string, the pipe string is discretized into spatial beam units, and all the beam units are assembled to obtain the overall equilibrium equation of the geometrically nonlinear analysis of the suspended pipe string:

(K ₀ +K _σ(u) )u=F, (3)

In the formula: K ₀ is the linear elastic stiffness matrix of the pipe string; K _σ is the geometric stiffness matrix of the pipe string, which is a function of the node displacement; u is the node displacement vector of the pipe string, including the constraint boundary conditions imposed on the upper and lower ends; F is Nodal force vector, including the suspension tension at the upper end of the pipe string, the unit length load of the pipe string and the axial pressure at the lower end of the pipe string;

The constraint boundary conditions imposed on the upper and lower ends are one of the following types of boundary conditions: (1) the upper end is hinged and the lower end is free; (2) the upper end is fixed and the lower end is free; (3) the upper end is free and the lower end is hinged; ( 4) The upper end is hinged, the lower end is hinged; (5) The upper end is fixed, the lower end is hinged; (6) The upper end is free, the lower end is fixed; (7) The upper end is hinged, the lower end is fixed; (8) The upper end is fixed, the lower end Fixing, to realize the calculation of the helical buckling critical load of the suspended pipe string in the vertical well with different constraint boundary conditions at the upper and lower ends;

Suspension tension is applied to the upper end, and its value can be any positive value, including suspension tension equal to 0; if the upper end of the pipe string is free, the suspension tension is 0; no matter what boundary condition is selected at the lower end of the pipe string, the axial displacement is constrained, and the lower end of the pipe string The axial pressure is the constraint reaction force;

The buckling of the pipe string will be in contact with the wellbore. Considering the geometric nonlinearity and contact nonlinearity comprehensively, the overall equilibrium equation for the geometric nonlinearity and contact nonlinear static buckling analysis of the suspended pipe string is:

(K ₀ +K _σ(u) +K _n(u) )u=F+F _n(u) ; (4)

In the formula: K _n(u) is the contact stiffness matrix of the pipe string; F _n is the contact force vector of the pipe string, which is a function of the nodal displacement.

Step 3. Establish the helical buckling analysis method of the suspended pipe string:

The dynamics method is used to solve the problem of helical buckling analysis of suspended pipe strings in vertical wells. The basic kinetic equation of helical buckling of suspended pipe strings is:

Mu"+Cu'+Ku=F(t); (5)

In the formula: M is the mass matrix of the pipe string; C is the damping matrix of the pipe string; K is the stiffness matrix of the pipe string, K=K ₀ +K _σ(u) +K _n(u) ; u′ is the node velocity vector ; u″ is the nodal acceleration vector; F(t) is the nodal load vector, including the suspension tension at the upper end of the pipe string, the unit length load of the pipe string, the axial pressure at the lower end of the pipe string and the contact force of the pipe string; t is the calculation time;

Step 4. Solve the helical buckling of the suspended pipe string:

Equation (5) is implicitly solved.

Step 5. Post-processing of the helical buckling calculation results of the suspended pipe string:

Extract the lateral displacement of each node of the pipe string in two directions, and then calculate the lateral deformation displacement and circumferential angle of each node of the pipe string; if the helical angle between the pipe string and the upper and lower contact points of the wellbore is not equal to 360°, change the upper suspension tension , and change the damping ratio and time increment, repeat step 4 and calculate repeatedly until the helix angle is 360°;

According to the calculation results, the dimensionless total length ξ _L of the suspended pipe string is divided into four sections, namely, the lower compression section ξ _C1 , the compression helical section ξ _C2 , the upper compression section ξ _C3 , and the tension section ξ _T , where the compression section The dimensionless length is:

ξ _C ＝ ξ _C1 + ξ _C2 + ξ _C3 , (10)

The dimensionless total length of the pipe string is:

ξ _L = ξ _C + ξ _T ; (11)

Step 6. Determine the helical buckling critical load of the suspended pipe string:

Considering the constraint boundary conditions at the upper and lower ends of the actual suspended pipe string and the influence of the length of the pipe string in the suspended tension section on helical buckling, the critical load of helical buckling should be ξ _C1 of the lower section under compression, ξ _C2 of the helical section under compression and ξ _C3 of the upper section under compression The sum of the weight to the axial pressure at the lower end, not the axial pressure at the lower end corresponding to the weight of the compressed helical section ξ _C2 Therefore, the helical buckling critical load of the suspended pipe string is:

where: _ξC is the dimensionless critical load for the helical buckling of the suspended pipe string.

The implicit calculation of equation (5) in step 4 of the above scheme includes:

The large-scale general-purpose finite element analysis software ANSYS is used, the BEAM188 element is selected as the space beam element, the CONTA176 contact element and the TARGE170 target element are respectively selected for the contact between the pipe string and the wellbore, and the equation (5) is implicitly solved and calculated:

a. Selection of damping ratio:

The α damping is selected in the damping matrix C of equation (5), considering the first-order natural frequency of the pipe string, the α damping formula is

In the formula: is the modal damping ratio of the pipe string, using overdamping, the damping ratio ω is the first-order natural frequency of the string;

b. Selection of time increment:

The selection principle for calculating the time increment in the direct integration method is: the normal time increment takes 1/40 times the natural period, the minimum time increment takes 1/200 times the natural period, and the maximum time increment takes 1/10 times the natural period;

c. Selection and application of initial defects:

The initial defect selects the initial disturbance force, and the different application methods of the disturbance force affect the handedness of the final helical section of the helical buckling. The handedness can be left-handed or right-handed; A transverse disturbance force is applied at the midpoint of the compression section, referred to as one disturbance force; (2) A transverse disturbance force is applied at the midpoint of the compression section of the pipe string, and a disturbance torque is applied at the upper end, referred to as two disturbance forces; (3 ) At 1/4, 2/4 and 3/4 of the pressure section of the pipe string, respectively apply transverse disturbance forces at 90° to each other, referred to as three disturbance forces;

The magnitude of the applied disturbance force is the unit load, and the time history of the application of the disturbance force is: the calculation time is 1/2 times the natural period of the pipe string, and the disturbance force of 180° sine wave is applied; the calculation time is 1/2 times the natural period of the pipe string After the period, the applied disturbance force is 0;

d. External load application

The time history of the application of the suspension tension at the upper end is as follows: (1) the calculation time is before 1/4 times the natural period of the pipe string, and the 90° sine wave suspension tension is applied; (2) the calculation time is after 1/4 times the natural period of the pipe string, apply a constant suspension tension;

The load per unit length of the pipe string is applied by gravity acceleration, and its time history is: (1) the calculation time is before 1/4 times the natural period of the pipe string, and the gravity acceleration of 90° sine wave is applied; (2) the calculation time is 1/4 of the pipe string After /4 times the natural period, a constant gravitational acceleration is applied;

e. Calculate the total time

The Newmark direct integration method is used to carry out the implicit finite element calculation of the string dynamic equation in formula (5). The total calculation time is more than 10 natural periods of the pipe string, so that the displacement of each node of the pipe string tends to be stable, the velocity and acceleration of each node of the pipe string tend to be zero, and equation (5) degenerates into equation (4), realizing the slow dynamic analysis method to solve the static buckling of pipe strings.

The present invention has the following beneficial effects:

1. The present invention considers the influence of the length of the suspended pipe string and the constraint boundary conditions, dimensionless the length of the pipe string and the critical load, and provides a general method for determining the helical buckling critical load of the suspended pipe string in vertical wells. The pipe string is one of the drill string, casing string, test pipe string, sucker rod string and coiled tubing in petroleum drilling and production engineering, and the specification, size and total length of the pipe string are arbitrary values.

2. The method for determining the helical buckling critical load of a suspended pipe string in a vertical well provided by the present invention has the characteristics of stable algorithm, fast calculation efficiency, and high accuracy of results, which makes it more in line with engineering practice and is used to guide the placement position of centralizers, reducing Minimize or avoid the damage of helical buckling to the oil drilling and production string, and improve the engineering technology application level of the oil drilling and production string.

Description of drawings

Figure 1 shows the helical buckling configuration characteristics of the suspended pipe string. The constraint boundary condition is that the upper and lower ends are hinged, the upper end is suspended to apply tension, the lower end is axially restrained, and the lower end restraint reaction force is the axial pressure caused by the self-weight of the compression section. The calculated dimensionless length ξ _L of the suspended pipe string is divided into four sections, namely, the lower compression section ξ _C1 , the compression helical section ξ _C2 , the upper compression section ξ _C3 and the tension section ξ _T . The dimensionless length of the pressure section is ξ _C ＝ ξ _C1 + ξ _C2 + ξ _C3 , and the dimensionless total length of the pipe string is ξ _L ＝ ξ _C + ξ _T .

Fig. 2 is part of the calculation results of the helical buckling curves for different lengths of suspended pipe strings and constraint boundary conditions. The x and y coordinates represent the lateral deflection of the pipe string, and the z coordinate represents the dimensionless length of the pipe string. It can be seen from the figure that the constraint boundary conditions at the upper and lower ends of the suspended pipe string and the length of the pipe string have an important influence on the helical buckling.

Fig. 3 shows the dimensionless critical load of helical buckling calculated under different lengths of suspended pipe strings and constraint boundary conditions. It can be seen from the figure that as the length of the pipe string increases, the critical load of helical buckling gradually decreases and tends to be stable; the upper end is restrained by fixed support and hinged support respectively, and the critical load tends to be equal when the lower end is restrained by the same kind, indicating that the upper end The influence of these two constraints on helical buckling tends to be the same; while the lower end constraint has an important influence on the critical load of helical buckling, and the critical load of the fixed-support constraint is greater than that of the hinge-support constraint. It can be seen that, given the constraint boundary conditions at the upper and lower ends of the suspended pipe string, the total length of the pipe string, the moment of inertia of the cross section (related to the inner and outer diameters of the pipe string), the load per unit length, and the elastic modulus of the pipe string material, the suspension pipe string can be determined. Critical load for helical buckling.

detailed description

Below in conjunction with accompanying drawing, the present invention will be further described:

The method for determining the helical buckling critical load of the vertical well suspended pipe string is as follows:

1. Suspension string parameter initialization

Input the geometric dimension parameters such as inner diameter D _i , outer diameter D _o and length L of the pipe string, input material parameters such as the elastic modulus E and density ρ _s of the pipe string, input the liquid density ρ _i inside the pipe string, and the liquid in the outer annulus of the pipe string For fluid physical parameters such as density ρ _o , input wellbore inner diameter D _I .

According to the density of the pipe string and the density of the liquid inside and outside the pipe string, the load q per unit length of the pipe string is obtained as

The length of the pipe string is dimensionless, and the dimensionless length ξ _L of the pipe string is

2. Establish the buckling balance equation of the suspended pipe string

With the above string-related initialization input parameters, if the string is discretized into spatial solid units, the model will be too large and the calculation efficiency will be low. Since the axial dimension of the pipe string is much larger than its cross-sectional size, the pipe string is discretized into spatial beam units, which can significantly improve the calculation efficiency.

The pipe string is a large flexible rod or a slender rod. The upper end of the pipe string is suspended under tension, and the lower end of the pipe string is under compression. The stiffness of the pipe string under compression decreases. When the compression section reaches a certain length, the pipe string buckles and undergoes transverse bending deformation. , will produce large lateral displacement and rotation, the relationship between force and deformation is no longer linear, and the nonlinear effect is prominent, which belongs to the geometric nonlinear problem.

The spatial beam element matrix includes the elastic stiffness matrix and the geometric stiffness matrix After assembling all the units, the overall balance equation of the geometric nonlinear analysis of the suspended pipe string can be obtained as

(K ₀ +K _σ(u) )u=F, (3)

In the formula: K ₀ is the linear elastic stiffness matrix of the pipe string; K _σ is the geometric stiffness matrix of the pipe string, which is a function of the node displacement; u is the node displacement vector of the pipe string, including the constraint boundary conditions imposed on the upper and lower ends; F is Nodal force vector, including the suspension tension at the upper end of the pipe string, the load per unit length of the pipe string, and the axial pressure at the lower end of the pipe string.

The constraint boundary conditions imposed on the upper and lower ends are one of the following types of boundary conditions: (1) the upper end is hinged and the lower end is free; (2) the upper end is fixed and the lower end is free; (3) the upper end is free and the lower end is hinged; ( 4) The upper end is hinged, the lower end is hinged; (5) The upper end is fixed, the lower end is hinged; (6) The upper end is free, the lower end is fixed; (7) The upper end is hinged, the lower end is fixed; (8) The upper end is fixed, the lower end Fixed branch. Realize the calculation of the helical buckling critical load of the suspended pipe string in vertical wells with different constraint boundary conditions at the upper and lower ends.

Suspension tension is applied to the upper end, and its value can be any positive value, including suspension tension equal to 0. If the upper end of the string is free, the suspension tension is 0. No matter which boundary condition is selected at the lower end of the pipe string, the axial displacement is constrained, and the axial pressure at the lower end of the pipe string is the restraint reaction force.

In the process of transverse bending deformation, the pipe string will be restricted by the wellbore, and it will produce contact mechanical behavior with the inner wall of the wellbore at any axial distance and any circumferential direction, which belongs to the contact nonlinear problem. The geometric nonlinearity and contact nonlinearity need to be considered comprehensively, and the overall balance equation of the suspended pipe string geometric nonlinearity and contact nonlinear static buckling analysis

(K ₀ +K _σ(u) +K _n(u) )u=F+F _n(u) (4)

In the formula: K _n(u) is the contact stiffness matrix of the pipe string; F _n is the contact force vector of the pipe string, which is a function of the nodal displacement.

3. Establishment of helical buckling analysis method for suspended pipe strings

Equation (4) can be calculated by software programming, and can also be calculated by large-scale general-purpose finite element software (such as ANSYS software, ABAQUS software, etc.), but no matter what method is used for calculation, since equation (4) contains dual nonlinearities of geometry and contact, it can be There are problems of convergence difficulty and algorithm instability. There are strong nonlinear mechanical behaviors such as jumping changes in the buckling configuration of the pipe string, contact and separation between the pipe string and the wellbore, etc., which lead to sudden changes in the contact state during the calculation process, abnormal termination of the calculation, and convergence difficulties. The instability of the algorithm is manifested in the fact that the convergent solution is not unique, and there is randomness in the helical post-buckling configuration. For example, after the sinusoidal buckling configuration is formed, as the axial pressure load at the lower end of the pipe string increases, the sinusoidal buckling configuration rotates in the wellbore, but the helical buckling configuration cannot be formed; Sensitivity, sometimes helical buckling configuration can be formed, sometimes not; even if helical buckling configuration is formed, it returns to sinusoidal buckling configuration; at different axial distances in the same buckling configuration, There may be both left-helical and right-helical buckling configuration phenomena.

For this reason, a slow dynamic analysis method for nonlinear static buckling analysis of suspended pipe strings is proposed. This method aims at the problems of difficult buckling convergence of pipe strings and algorithm instability, using dynamic methods, applying all dead loads in a certain way, and considering time integration effects , set a larger damping value, calculate for a certain period of time, and solve the dynamic response of the pipe string until it stabilizes. That is to use the dynamic method to solve the problem of helical buckling analysis of suspended pipe strings in vertical wells.

The basic kinetic equation of the helical buckling of the suspended pipe string is

Mu″+Cu′+Ku=F(t) (5)

In the formula: M is the mass matrix of the pipe string; C is the damping matrix of the pipe string; K is the stiffness matrix of the pipe string, K=K ₀ +K _σ(u) +K _n(u) ; u′ is the node velocity vector ; u″ is the nodal acceleration vector; F(t) is the nodal load vector, including the suspension tension at the upper end of the pipe string, the load per unit length of the pipe string, the axial pressure at the lower end of the pipe string and the contact force of the pipe string; t is the calculation time.

4. Solution of helical buckling of suspended pipe string

The large-scale general-purpose finite element analysis software ANSYS is used to discretize the pipe column beam unit with BEAM188, and the wellbore with BEAM188 to create a three-dimensional beam-beam contact between the pipe string and the wellbore. The CONTA176 contact unit is attached to the outer surface of the pipe column beam unit, and the TARGE170 target unit is attached to the inner surface of the wellbore. The CONTA176 contact element and the TARGE170 target element have a line-line contact relationship, but have 3D contact features, which can be used to simulate the nonlinear problem of the circumferential contact between the pipe string and the wellbore.

Equation (5) is implicitly solved. The solution techniques of the helical buckling slow dynamic analysis method for suspended pipe strings include:

(1) Selection of damping ratio

The damping matrix C in equation (5) is

C=αM+βK, (6)

In the formula: α is the mass matrix coefficient, referred to as α damping; β is the stiffness matrix coefficient, referred to as β damping.

Usually the α and β of the pipe string are not known, and the modal damping ratio can be used Calculated to get. According to the principle of orthogonality, the modal damping ratio of the pipe string and the natural frequency ω satisfy the following formula

The natural frequency in the above formula usually takes the first order, for example, the first order natural frequency of a pipe column hinged at both ends is

In the formula: ρ is the density of the pipe string; A is the cross-sectional area of the pipe string.

Neglecting the influence of β damping and selecting the first-order natural frequency, the formula of α damping is

In the formula: is the modal damping ratio of the pipe string; ω is the natural frequency of the pipe string.

When calculating with the slow dynamic analysis method, a larger value should be selected for the α damping. If the actual α damping is directly calculated, the dynamic response time will be long and the calculation efficiency will be low. Therefore, by choosing a larger damping ratio Enlarge the α damping to shorten the time for the dynamic response to the steady state and improve the calculation efficiency. Using over damping, take the damping ratio Implements amplified alpha damping.

(2) Selection of calculation time increment

The selection of time increment will affect the calculation efficiency and accuracy, in order to improve the calculation accuracy. The selection principle for calculating the time increment in the direct integration method is as follows: the normal time increment is 1/40 times the natural period, the minimum time increment is 1/200 times the natural period, and the maximum time increment is 1/10 times the natural period.

(3) Selection of initial defects

Since the nonlinear buckling analysis requires that the pipe string is not "perfect", if the pipe string has no initial defects, the nonlinear buckling analysis cannot be performed. The initial defect can be the initial geometric defect of the pipe string. The eigenvalue buckling analysis can be performed first, and the node coordinates can be updated according to the extracted eigenvalue buckling mode to implement the initial geometric defect. The initial defect can also be to apply a small disturbance force to cause a slight lateral deflection deformation, and check whether the string buckles after the disturbance force is withdrawn.

The initial geometric imperfection will affect the critical buckling load of the string, while the small disturbance force is applied initially and canceled in the subsequent analysis, which will not affect the critical buckling load of the string. Using the initial disturbance force method not only maintains the integrity of the pipe string, but also realizes the application of initial defects.

Different application methods of perturbation force affect the handedness (left helical or dextral helical) of the final helical segment of helical buckling. The way to apply the initial disturbance force is one of the following: (1) Only apply a transverse disturbance force at the midpoint of the compression section of the pipe string, referred to as a disturbance force; (2) Apply a transverse disturbance force at the midpoint of the compression section of the pipe string One transverse disturbance force, one disturbance torque is applied on the upper end, referred to as two disturbance forces for short; (3) At 1/4, 2/4 and 3/4 of the pressure section of the pipe string, respectively apply transverse Disturbance force, referred to as three disturbance forces.

The magnitude of the applied disturbance force is the unit load, and the time history of the application of the disturbance force is: the calculation time is 1/2 times the natural period of the pipe string, and the disturbance force of 180° sine wave is applied; the calculation time is 1/2 times the natural period of the pipe string After a period, the applied disturbance force is 0.

(4) External load application

The time history of the application of the suspension tension at the upper end is as follows: (1) the calculation time is before 1/4 times the natural period of the pipe string, and the 90° sine wave suspension tension is applied; (2) the calculation time is after 1/4 times the natural period of the pipe string, Apply a constant suspension tension.

The load per unit length of the pipe string is applied by gravity acceleration, and its time history is: (1) the calculation time is before 1/4 times the natural period of the pipe string, and the gravity acceleration of 90° sine wave is applied; (2) the calculation time is 1/4 of the pipe string After /4 times the natural period, a constant gravitational acceleration is applied.

(5) Calculate the total time

The Newmark direct integration method is used to carry out the implicit finite element calculation of the string dynamic equation in formula (5). If the displacement, velocity and acceleration of the pipe string at time t are known, the dynamic response (displacement, velocity and acceleration, etc.) of the pipe string at time t+Δt can be calculated.

The total calculation time is more than 10 natural periods of the pipe string, so that the displacement of each node of the pipe string tends to be stable, the velocity and acceleration of each node of the pipe string tend to be zero, and equation (5) degenerates into equation (4), realizing the slow dynamic analysis method to solve the static buckling of pipe strings.

5. Post-processing of helical buckling calculation results of suspended pipe string

The lateral displacement in two directions of each node of the pipe string is extracted, and then the lateral deformation displacement and circumferential angle of each node of the pipe string are obtained. If the helix angle between the pipe string and the upper and lower contact points of the wellbore is not equal to 360°, change the suspension tension at the upper end, change the damping ratio and time increment, and repeat step 4 until the helix angle is 360°.

According to the calculation results, the dimensionless total length ξ _L of the suspended pipe string is divided into four sections (see Fig. 1), namely, the lower section under compression ξ _C1 , the helical section under compression ξ _C2 , the upper section under compression ξ _C3 and the section under tension ξ _T , where the dimensionless length of the compression section is

ξ _C ＝ ξ _C1 + ξ _C2 + ξ _C3 , (10)

The dimensionless total length of the pipe string is

ξ _L =ξ _C +ξ _T . (11)

6. Determination of helical buckling critical load of suspended pipe string

First, it is related to the length of the pipe string; second, it is related to the constraint boundary conditions at the upper and lower ends. Fig. 2 shows the calculation results of helical buckling curves for different lengths of suspended pipe strings and constrained boundary conditions. The x and y coordinates represent the lateral deflection of the pipe string, and the z coordinate represents the dimensionless length of the pipe string. Four types of constraint boundary conditions are used: (1) hinged support at the upper end - hinged support at the lower end; (2) fixed support at the upper end - hinged support at the lower end; (3) hinged support at the upper end - fixed support at the lower end; (4) fixed support at the upper end - fixed support at the lower end .

It can be seen from Fig. 2 that the constraint boundary conditions at the upper and lower ends of the suspended pipe string and the length of the pipe string have an important influence on the helical buckling.

Considering the constraint boundary conditions at the upper and lower ends of the actual suspended pipe string and the influence of the length of the pipe string on the helical buckling, according to the calculation results, the critical load of the helical buckling should be ξ _C1 of the lower section under compression, ξ _C2 of the helical section under compression and ξ _C3 of the upper section under compression The sum of weight to the axial pressure at the lower end, not the axial pressure at the lower end corresponding to the weight of the compressed helical section ξ _C2 itself Therefore, the helical buckling critical load of the suspended pipe string is

where: _ξC is the dimensionless critical load for the helical buckling of the suspended pipe string.

According to the above steps, the critical load of the helical buckling of the suspended pipe string can be determined by knowing the constraint boundary conditions at the upper and lower ends of the suspended pipe string, the total length of the pipe string, the moment of inertia of the cross section, the load q per unit length, and the elastic modulus of the pipe string material .

According to the present invention, some calculation results of the helical buckling under different lengths and boundary constraint conditions of the suspended pipe string are shown in Table 1.

Table 1 Partial calculation results of helical buckling under different lengths and boundary constraints of suspended pipe strings

It can be seen from Table 1 that when the boundary constraint condition of the suspended pipe string is upper-end hinged support-lower end hinged support, the dimensionless total length of the pipe string is ξ _L = 8, and the obtained dimensionless compression lower section ξ _C1 = 0.929, dimensionless compression The helical section ξ _C2 = 4.617, the dimensionless compression upper section ξ _C3 = 1.876, the dimensionless tension section ξ _T = 0.578, the total length of the dimensionless compression section ξ _C = 7.422, and the critical load is

Table 1 can be used to calculate the helical buckling critical load of different specifications and sizes of suspended pipe strings. For example, a drill collar is used for the suspension pipe string, the outer diameter is 158.75mm, the inner diameter of the drill collar is 57.15mm, the elastic modulus E=2.1E11Pa, q=1149.0N/m, and the dimensionless unit length It can be obtained from Table 1:

(1) Boundary constraint conditions take the upper hinged support - lower hinged support, the dimensionless total length of the pipe string is ξ _L = 8, the total length of the pipe string Under pressure Compressed helical section Upper section under pressure Tension section suspension tension Total length of compression section helical buckling critical load

(2) Boundary constraint conditions take the upper hinged support - lower hinged support, the dimensionless total length of the pipe string is ξ _L = 30, the total length of the pipe string Tension section suspension tension Total length of compression section helical buckling critical load

Fig. 3 shows the helical buckling dimensionless critical loads for different lengths of suspended pipe strings and constrained boundary conditions. It can be seen from Fig. 3 that with the increase of the dimensionless length of the pipe string, the dimensionless critical load of helical buckling gradually decreases and tends to be stable; The load tends to be equal, indicating that the influence of the two upper constraints on the helical buckling tends to be the same; while the lower constraint has an important influence on the dimensionless critical load of the helical buckling, and the critical load of the fixed restraint is greater than that of the hinged restraint.

In order to verify the calculation accuracy of the method for determining the helical buckling critical load of the suspended pipe string, the constraint boundary conditions are changed, that is, the lower end is hinged and the upper end is free, and the calculation is performed again. Since the critical load calculated in the literature generally does not consider the influence of boundary constraints, the compression load corresponding to the helical section's own weight is taken as the critical load, which is consistent with the constraint boundary conditions of the compression helical section ξ _C2 freely calculated at the upper end unanimous. Under the constraint boundary condition of hinged support at the lower end and freedom at the upper end, the dimensionless length of the compressed helical section ξ _C2 of the present invention is 5.597, while Academician Gao Deli (2006) used the energy method to obtain a dimensionless length of 5.62, with a relative error of 0.4%. Through the comparison, it can be deduced that the present invention considers the influence of the length of the suspended pipe string and the constraint boundary conditions, and the determined helical buckling critical load of the suspended pipe string in vertical wells is more in line with engineering practice, and has the characteristics of stable algorithm, fast calculation efficiency, and high result accuracy.

Claims (3)

1. A method for determining the helical buckling critical load of a vertical well suspended pipe string, characterized in that: the method for determining the helical buckling critical load of the vertical well suspended pipe string: Step 1. Suspension string parameter initialization: Using the parameters of the suspended pipe string, according to the density of the pipe string and the density of the liquid inside and outside the pipe string, the load q per unit length of the pipe string is obtained as: <mrow> <mi>q</mi> <mo>=</mo> <mfrac> <mi>&amp;pi;</mi> <mn>4</mn> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>D</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>&amp;rho;</mi> <mi>s</mi> </msub> <mi>g</mi> <mo>+</mo> <mfrac> <mi>&amp;pi;</mi> <mn>4</mn> </mfrac> <msubsup> <mi>D</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mi>g</mi> <mo>-</mo> <mfrac> <mi>&amp;pi;</mi> <mn>4</mn> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>D</mi> <mi>I</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>D</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>&amp;rho;</mi> <mi>o</mi> </msub> <mi>g</mi> <mo>;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> Dimensionless the length of the pipe string, the dimensionless total length ξ _L of the pipe string can be obtained as: <mrow> <msub> <mi>&amp;xi;</mi> <mi>L</mi> </msub> <mo>=</mo> <mfrac> <mi>L</mi> <mroot> <mrow> <mi>E</mi> <mi>I</mi> <mo>/</mo> <mi>q</mi> </mrow> <mn>3</mn> </mroot> </mfrac> <mo>;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> The parameters of the suspended pipe string include pipe string geometric dimension parameters, pipe string material parameters, fluid physical parameters and wellbore inner diameter D _I , the pipe string geometric dimension parameters include inner diameter D _i , outer diameter D _o and length L, and the pipe string material parameters include String elastic modulus E and density ρ _s ; fluid physical parameters include liquid density ρ _i inside the string, liquid density ρ _o outside the string, and I is the moment of inertia; Step 2: Establish the buckling equilibrium equation of the suspended pipe string: Using the initialization parameters of the suspended pipe string, the pipe string is discretized into spatial beam units, and all the beam units are assembled to obtain the overall equilibrium equation of the geometrically nonlinear analysis of the suspended pipe string: (K ₀ +K _σ(u) )u=F, (3) where K ₀ is the linear elastic stiffness matrix of the pipe string; K _σ is the geometric stiffness matrix of the pipe string, which is a function of the node displacement; u is the nodal displacement vector of the pipe string, including the constraint boundary conditions applied at the upper and lower ends; F is the nodal force vector, including the suspension tension at the upper end of the pipe string, the unit length load of the pipe string and the axial pressure at the lower end of the pipe string; The constraint boundary conditions imposed on the upper and lower ends are one of the following types of boundary conditions: (1) the upper end is hinged and the lower end is free; (2) the upper end is fixed and the lower end is free; (3) the upper end is free and the lower end is hinged; ( 4) The upper end is hinged, the lower end is hinged; (5) The upper end is fixed, the lower end is hinged; (6) The upper end is free, the lower end is fixed; (7) The upper end is hinged, the lower end is fixed; (8) The upper end is fixed, the lower end Fixing, to realize the calculation of the helical buckling critical load of the suspended pipe string in the vertical well with different constraint boundary conditions at the upper and lower ends; Suspension tension is applied to the upper end, and its value is any positive value, including suspension tension equal to 0; if the upper end of the pipe string is free, the suspension tension is 0; no matter what boundary condition is selected at the lower end of the pipe string, the axial displacement is constrained, and the axis of the lower end of the pipe string The directional pressure is the constraint reaction force; The buckling of the pipe string will be in contact with the wellbore. Considering the geometric nonlinearity and contact nonlinearity comprehensively, the overall equilibrium equation for the geometric nonlinearity and contact nonlinear static buckling analysis of the suspended pipe string is: (K ₀ +K _σ(u) +K _n(u) )u=F+F _n(u) ; (4) where K _n(u) is the contact stiffness matrix of the pipe string; F _n is the contact force vector of the pipe string, which is a function of the nodal displacement; Step 3. Establish the helical buckling analysis method of the suspended pipe string: The dynamics method is used to solve the problem of helical buckling analysis of suspended pipe strings in vertical wells. The basic kinetic equation of helical buckling of suspended pipe strings is: Mu"+Cu'+Ku=F(t); (5) In the formula: M is the mass matrix of the pipe string; C is the damping matrix of the pipe string; K is the stiffness matrix of the pipe string, K=K ₀ +K _σ(u) +K _n(u) ; u′ is the node velocity vector ; u″ is the nodal acceleration vector; F(t) is the nodal load vector, including the suspension tension at the upper end of the pipe string, the unit length load of the pipe string, the axial pressure at the lower end of the pipe string and the contact force of the pipe string; t is the calculation time; Step 4. Solve the helical buckling of the suspended pipe string: Carry out implicit solution calculation to equation (5); Step 5. Post-processing of the helical buckling calculation results of the suspended pipe string: Extract the lateral displacement of each node of the pipe string in two directions, and then calculate the lateral deformation displacement and circumferential angle of each node of the pipe string; if the helical angle between the pipe string and the upper and lower contact points of the wellbore is not equal to 360°, change the upper suspension tension , and change the damping ratio and time increment, repeat step 4 and calculate repeatedly until the helix angle is 360°; According to the calculation results, the dimensionless total length ξ _L of the suspension pipe string is divided into four sections, which are the lower compression section ξ _C1 , the compression helical section ξ _C2 , the upper compression section ξ _C3 and the tension section ξ _T . The class length is: ξ _C ＝ ξ _C1 + ξ _C2 + ξ _C3 , (10) The dimensionless total length of the pipe string is: ξ _L = ξ _C + ξ _T ; (11) Step 6. Determine the helical buckling critical load of the suspended pipe string: Considering the constraint boundary conditions at the upper and lower ends of the actual suspended pipe string and the influence of the length of the pipe string in the suspended tension section on helical buckling, the critical load of helical buckling should be ξ _C1 of the lower section under compression, ξ _C2 of the helical section under compression and ξ _C3 of the upper section under compression The sum of weight to the axial pressure at the lower end, not the axial pressure at the lower end corresponding to the weight of the compressed helical section ξ _C2 itself Therefore, the helical buckling critical load of the suspended pipe string is: <mrow> <msub> <mi>F</mi> <mrow> <mi>h</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;xi;</mi> <mi>C</mi> </msub> <mroot> <mrow> <msup> <mi>EIq</mi> <mn>2</mn> </msup> </mrow> <mn>3</mn> </mroot> <mo>;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> where: _ξC is the dimensionless length of the compression section. 2. the method for determining the helical buckling critical load of the vertical well suspended pipe string according to claim 1, is characterized in that: carrying out implicit solution calculation to equation (5) in step 4 comprises: The large-scale general-purpose finite element analysis software ANSYS is used, the BEAM188 element is selected as the space beam element, the CONTA176 contact element and the TARGE170 target element are respectively selected for the contact between the pipe string and the wellbore, and the equation (5) is implicitly solved and calculated: a. Selection of damping ratio: The α damping is selected in the damping matrix C of equation (5), considering the first-order natural frequency of the pipe string, the α damping formula is: In the formula: is the modal damping ratio of the pipe string, using overdamping, the damping ratio ω is the first-order natural frequency of the string; b. Selection of time increment: The selection principle for calculating the time increment in the direct integration method is: the normal time increment takes 1/40 times the natural period, the minimum time increment takes 1/200 times the natural period, and the maximum time increment takes 1/10 times the natural period; c. Selection and application of initial defects: The initial defect selects the initial disturbance force, and the different application methods of the disturbance force affect the handedness of the final helical section of the helical buckling. The handedness can be left-handed or right-handed; A transverse disturbance force is applied at the midpoint of the compression section, referred to as one disturbance force; (2) A transverse disturbance force is applied at the midpoint of the compression section of the pipe string, and a disturbance torque is applied at the upper end, referred to as two disturbance forces; (3 ) At 1/4, 2/4 and 3/4 of the pressure section of the pipe string, respectively apply transverse disturbance forces at 90° to each other, referred to as three disturbance forces; The magnitude of the applied disturbance force is the unit load, and the time history of the application of the disturbance force is: the calculation time is 1/2 times the natural period of the pipe string, and the disturbance force of 180° sine wave is applied; the calculation time is 1/2 times the natural period of the pipe string After the period, the applied disturbance force is 0; d. External load application: The time history of the application of the suspension tension at the upper end is as follows: (1) the calculation time is before 1/4 times the natural period of the pipe string, and the suspension tension of 90° sine wave is applied; (2) the calculation time is after 1/4 times the natural period of the pipe string, apply a constant suspension tension; The load per unit length of the pipe string is applied through the acceleration of gravity, and its time history is as follows: (1) the calculation time is before 1/4 times the natural period of the pipe string, and the gravity acceleration of 90° sine wave is applied; (2) the calculation time is before the pipe string 1 After /4 times the natural period, a constant gravitational acceleration is applied; e. Calculate the total time: Using the Newmark direct integration method, the implicit finite element calculation of the pipe string dynamic equation in (5) is carried out. The node velocity and acceleration tend to 0, and Equation (5) degenerates into Equation (4), realizing the solution to the static buckling of the pipe string by using the slow dynamic analysis method. 3. the method for determining the helical buckling critical load of vertical well suspended pipe string according to claim 2, is characterized in that: the pipe string in the step 1 is drill string, casing string, test pipe string, One of the sucker rod string and coiled tubing, the specification, size and total length of the string are arbitrary values.