CN102289536A - Method for analyzing transverse force bending with parameters of vertical pipe of deep water drilling well - Google Patents

Abstract

The invention relates to a method for researching an ocean deep water vertical pipe, in particular to a method for analyzing transverse force bending with parameters of a vertical pipe of a deep water drilling well. The method takes influence of the vertical movement of the vertical pipe of the deep water drilling well on bending deformation into consideration. Compared with the conventional method, the method provided by the invention more accords with the actual stress and deformation states of the vertical pipe of the deep water drilling well; and by the method, the defect of insecurity of the prior art is overcome, so the analysis of the transverse force bending with the parameters of the vertical pipe of the deep water drilling well more accords with reality.

Description

A kind of deepwater drilling standpipe parameter transversal force bending analysis method

Technical field

The present invention relates to the research method of ocean deepwater standpipe, be specifically related to a kind of deepwater drilling standpipe parameter transversal force bending analysis method.

Background technology

The deepwater drilling standpipe is a kind of main type of deep water marine riser, and the lower end of standpipe is connected with subsea wellheads, and wall tension acts directly on the well head, and the fluid in the pipe passes standpipe from the seabed continuously and flows to floating platform.Deepwater drilling standpipe two ends flexibly connect by flexible joint and subsea wellheads and drilling platform, and the deepwater drilling platform has semisubmersible and two kinds of structures of ship shape, and it is bigger that they vertical swings motion amplitude, therefore, causes that the drilling riser pipe top produces bigger vertical displacement.Because the effect of marine environment load, drilling riser pipe will produce transversal force (action direction of wave stream is perpendicular to the standpipe axis) bending, therefore, the part of riser top ends vertical displacement causes the standpipe axial deformation, and another one will cause standpipe flexural deformation (similar to the pressure bar stabilization problem).

Existing deepwater drilling standpipe bending analysis method is on complicated bend (considering the transversal force bending of the axial force) theoretical foundation that is based upon beam, the flexural deformation that is standpipe only is the transversal force flexural deformation that is caused by the environmental load (wave stream load) perpendicular to standpipe, that is:

$\frac{{\∂}^2}{\∂x^2}\left(\mathrm{EI}\frac{{\∂}^{2}y}{\∂x^2}\right)-\frac{\∂}{\∂x}\left(T\frac{\∂y}{\∂x}\right)=q\left(x\right)---\left(1\right)$

In the formula: y is the displacement of standpipe transverse curvature;

X is the axial coordinate of standpipe;

EI is a standpipe xsect bendind rigidity;

T is a standpipe tension force;

Q (x) is for acting on the fluid load on the standpipe.

Formula (1) is the BENDING DIFFERENTIAL EQUATION of deepwater drilling standpipe, and it does not consider the flexural deformation that the riser top ends vertical displacement causes.Thereby for having than the flexible bigger deepwater drilling standpipe of high-fineness ratio, such consideration is irrational.

As everyone knows, when an end of rod member produces axial displacement, under two kinds of conditions, rod member will bend, and the one, the axial displacement of end is bigger, and the axial deformation of rod member is not enough to the axial displacement of end all is converted into the strain energy of rod member; The 2nd, the bending stiffness of rod member is less or have initial bending to be out of shape.

The major defect of existing deepwater drilling standpipe parameter transversal force bending analysis method is as follows:

The slenderness ratio of deepwater drilling standpipe is big (1000～5000), therefore, and its axial rigidity

And bending stiffness

All less.And the rod member slenderness ratio (10～50) of the complicated bend theoretical research of beam is far smaller than the deepwater drilling standpipe, and the theoretical negligible axial distortion of traditional beam deflection, because the suffered axial action (power or displacement) of traditional girder construction is less.But the loading characteristic of deepwater drilling standpipe is different with the pressure bar stabilization problem with traditional girder construction with boundary condition, the deepwater drilling standpipe is subjected to the effect of axial tensile force and lateral load, if according to the stress condition analysis, the two ends that cause except that bending the displacement, can not produce the two ends displacement in opposite directions that other factors causes in opposite directions.But the top of deepwater drilling standpipe produces bigger vertical displacement owing to floating platform vertical swings motion, make the standpipe two ends produce displacement in opposite directions (being similar to compression rod), and the amplitude of vertical displacement has exceeded small deformation scope (can reach several meters).Therefore, prior art is not considered the bending that the vertical displacement of riser top ends causes, and adopts the buckling problem of the complicated bend theoretical analysis deepwater drilling standpipe of beam, and its analysis result is relatively unsafe.

Summary of the invention

The objective of the invention is to defective, a kind of deepwater drilling standpipe parameter transversal force bending analysis method is provided, make the bending analysis of deepwater drilling standpipe more realistic at prior art.

Technical scheme of the present invention is as follows: a kind of deepwater drilling standpipe parameter transversal force bending analysis method, and this method is considered environmental load and riser top ends vertical displacement simultaneously, the deepwater drilling standpipe BENDING DIFFERENTIAL EQUATION that provides is as follows:

$\frac{{\∂}^2}{\∂x^2}\left(\mathrm{EI}\frac{{\∂}^{2}y}{\∂x^2}\right)-\frac{\∂}{\∂x}\left(T\frac{\∂y}{\∂x}\right)=q\left(x\right)+\frac{\mathrm{GA}}{2}\frac{\∂u}{\∂x}$

In the formula: y is the displacement of standpipe transverse curvature;

X is the axial coordinate of standpipe;

EI is a standpipe xsect bendind rigidity;

T is a standpipe tension force;

Q (x) is for acting on the fluid load on the standpipe;

GA is a standpipe cross section shearing rigidity;

U is the standpipe vertical displacement, herein,

ε x is axial strain;

Utilize above-mentioned equation, calculate the bending stress of standpipe.

Further, aforesaid deepwater drilling standpipe parameter transversal force bending analysis method, the detailed process that this method is calculated the standpipe bending stress is as follows:

(1) standpipe is divided into several unit;

(2) displacement function of unit is expressed as the form of interpolating function:

u＝[S]{η}，

y＝[N]{a}，

In the formula, [S] is the axial displacement interpolating function,

{ η } is node axial displacement column vector,

[N] is the transversal displacement interpolating function,

{ a} is a node transversal displacement column vector;

(3) adopt the golden method of gal the Liao Dynasty, it is as follows that deepwater drilling standpipe BENDING DIFFERENTIAL EQUATION is converted to matrix equation:

[K]{a}＝{F}

In the formula:

Stiffness matrix

Load vector

{ a} is a node transversal displacement column vector;

L is an element length;

N is an element number;

(4), calculate the stiffness matrix of standpipe with the expression formula of stiffness matrix [K] in the tension force T substitution step (3) of standpipe;

(5) hang down based on floating platform and swing the vertical displacement vector { η } that motion calculation goes out riser top ends;

(6) with riser top ends vertical displacement vector { η } substitution load vector { the expression formula calculating load vector of F} that calculates in the step (5);

(7) { matrix equation in the F} substitution step (3) calculates the node transversal displacement column vector { a} of standpipe with the stiffness matrix [K] of standpipe and load vector;

(8) with the node transversal displacement column vector of standpipe a} and unit interpolating function [N] substitution following formula can calculate the transverse curvature line of deflection of standpipe:

y＝[N]{a}；

(9) the standpipe transverse curvature line of deflection substitution following formula that obtains in the step (8) is calculated bending stress:

$\left\{\mathrm{\σ}\right\}=\frac{\mathrm{EI}}{W}\left[N^{\′\′}\right]\left\{a\right\}$

In the following formula: W is a standpipe cross section bending modulus,

D is the standpipe external diameter.

Beneficial effect of the present invention is as follows: the present invention is in deepwater drilling standpipe parameter transversal force bending analysis, considered that deepwater drilling standpipe vertical motion is to diastrophic influence, the actual loading and the deformation state that more meet the deepwater drilling standpipe than existing method, overcome prior art and be partial to unsafe shortcoming, made deepwater drilling standpipe parameter transversal force bending analysis more realistic.

Description of drawings

Fig. 1 is a deepwater drilling standpipe parameter transversal force bending analysis method flow diagram of the present invention.

Embodiment

Describe the present invention below in conjunction with the drawings and specific embodiments.

Deepwater drilling standpipe two ends are connected with drilling platform with subsea wellheads by flexible joint, and the deepwater drilling platform has semisubmersible and two kinds of structures of ship shape, and it is bigger that they vertical swings motion amplitude, therefore, cause that the drilling riser pipe top produces bigger vertical displacement.Because the effect of marine environment load, drilling riser pipe will produce transversal force (action direction of wave stream is perpendicular to the standpipe axis) bending, therefore, the part of riser top ends vertical displacement causes the standpipe axial deformation, and another one will cause standpipe flexural deformation (similar to the pressure bar stabilization problem).Prior art is not considered the flexural deformation that the riser top ends vertical displacement causes, therefore, present drilling riser pipe bending analysis is based upon on traditional transversal force flexure theory basis fully.Because motion is swung in hanging down significantly of the big flexibility of deepwater drilling standpipe and drilling platform, it is irrational only drilling riser pipe being carried out the transversal force bending analysis, also is unsafe, because it has underestimated flexural deformation, thereby has underestimated bending stress.The present invention has considered the influence of the big displacement of deepwater drilling riser top ends to the transversal force bending, has proposed deepwater drilling standpipe parameter transversal force coupling bending analysis method.

The present invention adopts the deepwater drilling standpipe BENDING DIFFERENTIAL EQUATION of considering environmental load and riser top ends vertical displacement simultaneously, and is specific as follows:

$\frac{{\∂}^2}{\∂x^2}\left(\mathrm{EI}\frac{{\∂}^{2}y}{\∂x^2}\right)-\frac{\∂}{\∂x}\left(T\frac{\∂y}{\∂x}\right)=q\left(x\right)+\frac{\mathrm{GA}}{2}\frac{\∂u}{\∂x}---\left(2\right)$

In the formula: y is the displacement of standpipe transverse curvature;

X is the axial coordinate of standpipe;

EI is a standpipe xsect bendind rigidity;

T is a standpipe tension force;

Q (x) is for acting on the fluid load on the standpipe;

GA is a standpipe cross section shearing rigidity;

U is the standpipe vertical displacement, u=(x), herein,

ε _xBe axial strain;

In the formula (2),

The transverse force that causes for the riser top ends vertical displacement.

The concrete steps of standpipe parameter transversal force bending analysis are as follows:

(S1) standpipe is divided into several unit;

(S2) displacement function of unit is expressed as the form of interpolating function:

u＝[S]{η} (3)

y＝[N]{a} (4)

In the formula, [S] is the axial displacement interpolating function,

{ η } is node axial displacement column vector,

[N] is the transversal displacement interpolating function,

{ a} is a node transversal displacement column vector;

(S3) adopt gal the Liao Dynasty golden method (this is the common practise of this area),

(this formula is revised)

In the following formula, L is the total length of standpipe, and δ y is the variation of bending displacement, and the effect in formula (5) is a weight function, and this is a common practise;

It is as follows that deepwater drilling standpipe BENDING DIFFERENTIAL EQUATION (formula (2)) is converted to matrix equation:

[K]{a}＝{F} (6)

In the formula:

Stiffness matrix

Load vector

{ a} is a node transversal displacement column vector;

L is an element length;

N is an element number;

(S4), calculate the stiffness matrix of standpipe with the expression formula (formula (7)) of stiffness matrix [K] in tension force T (obtain according to the design top coefficient of tension, be known technology) the substitution step (S3) of standpipe;

(S5) hang down based on floating platform and swing the vertical displacement vector { η } (this is known technology) that motion calculation goes out riser top ends;

(S6) with riser top ends vertical displacement vector { η } substitution load vector { expression formula of F} (formula (8)) the calculating load vector that calculates in the step (S5);

(S7) { matrix equation in the F} substitution step (S3) (formula (6)) calculates the node transversal displacement column vector { a} of standpipe with the stiffness matrix [K] of standpipe and load vector;

(S8) with the node transversal displacement column vector of standpipe a} and unit interpolating function [N] substitution formula (4) can calculate the transverse curvature line of deflection of standpipe:

y＝[N]{a}；

(S9) the standpipe transverse curvature line of deflection substitution following formula (9) that obtains in the step (S8) is calculated bending stress:

$\left\{\mathrm{\σ}\right\}=\frac{\mathrm{EI}}{W}\left[N^{\′\′}\right]\left\{a\right\}---\left(9\right)$

In the following formula: W is a standpipe cross section bending modulus,

D is the standpipe external diameter.

The present invention has considered deepwater drilling standpipe vertical motion to diastrophic influence, more meets the actual loading and the deformation state of deepwater drilling standpipe than existing method, has overcome prior art and has been partial to unsafe shortcoming.

Obviously, those skilled in the art can carry out various changes and modification to the present invention and not break away from the spirit and scope of the present invention.Like this, if of the present invention these are revised and modification belongs within the scope of claim of the present invention and equivalent technology thereof, then the present invention also is intended to comprise these changes and modification interior.

Claims (2)

1. deepwater drilling standpipe parameter transversal force bending analysis method, it is characterized in that: this method is considered environmental load and riser top ends vertical displacement simultaneously, the deepwater drilling standpipe BENDING DIFFERENTIAL EQUATION that provides is as follows:

$\frac{{\∂}^2}{\∂x^2}\left(\mathrm{EI}\frac{{\∂}^{2}y}{\∂x^2}\right)-\frac{\∂}{\∂x}\left(T\frac{\∂y}{\∂x}\right)=q\left(x\right)+\frac{\mathrm{GA}}{2}\frac{\∂u}{\∂x}$

In the formula: y is the displacement of standpipe transverse curvature;

X is the axial coordinate of standpipe;

EI is a standpipe xsect bendind rigidity;

T is a standpipe tension force;

Q (x) is for acting on the fluid load on the standpipe;

GA is a standpipe cross section shearing rigidity;

U is the standpipe vertical displacement, herein, ε _xBe axial strain;

Utilize above-mentioned equation, calculate the bending stress of standpipe.

2. deepwater drilling standpipe parameter transversal force bending analysis method as claimed in claim 1 is characterized in that: the detailed process that this method is calculated the standpipe bending stress is as follows:

(1) standpipe is divided into several unit;

(2) displacement function of unit is expressed as the form of interpolating function:

u＝[S]{n}，

y＝[N]{a}，

In the formula, [S] is the axial displacement interpolating function,

{ η } is node axial displacement column vector,

[N] is the transversal displacement interpolating function,

{ a} is a node transversal displacement column vector;

(3) adopt the golden method of gal the Liao Dynasty, it is as follows that deepwater drilling standpipe BENDING DIFFERENTIAL EQUATION is converted to matrix equation:

[K]{a}＝{F}

In the formula:

Stiffness matrix

Load vector

{ a} is a node transversal displacement column vector;

L is an element length;

N is an element number;

(4), calculate the stiffness matrix of standpipe with the expression formula of stiffness matrix [K] in the tension force T substitution step (3) of standpipe;

(5) hang down based on floating platform and swing the vertical displacement vector { η } that motion calculation goes out riser top ends;

(6) with riser top ends vertical displacement vector { η } substitution load vector { the expression formula calculating load vector of F} that calculates in the step (5);

(7) { matrix equation in the F} substitution step (3) calculates the node transversal displacement column vector { a} of standpipe with the stiffness matrix [K] of standpipe and load vector;

(8) with the node transversal displacement column vector of standpipe a} and unit interpolating function [N] substitution following formula can calculate the transverse curvature line of deflection of standpipe:

y＝[N]{a}；

(9) the standpipe transverse curvature line of deflection substitution following formula that obtains in the step (8) is calculated bending stress:

$\left\{\mathrm{\σ}\right\}=\frac{\mathrm{EI}}{W}\left[N^{\′\′}\right]\left\{a\right\}$

In the following formula: W is a standpipe cross section bending modulus,

D is the standpipe external diameter.

Images