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CN111428384B - Mechanical analysis method of discontinuous directional rotary steering drilling tool assembly - Google Patents

Mechanical analysis method of discontinuous directional rotary steering drilling tool assembly Download PDF

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CN111428384B
CN111428384B CN202010318959.5A CN202010318959A CN111428384B CN 111428384 B CN111428384 B CN 111428384B CN 202010318959 A CN202010318959 A CN 202010318959A CN 111428384 B CN111428384 B CN 111428384B
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point
eiy
bending moment
drilling tool
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CN111428384A (en
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夏成宇
王志亮
范宇
吴鹏程
王旭东
钱利勤
黄剑
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Shandong Weima Equipment Technology Co Ltd
Yangtze University
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Shandong Weima Equipment Technology Co ltd
Yangtze University
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B7/00—Special methods or apparatus for drilling
    • E21B7/04—Directional drilling

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Abstract

The invention relates to the field of oil and gas drilling, in particular to a mechanical analysis method of a discontinuous directional rotary steering drilling tool assembly. The invention adopts the thought of a infinitesimal method and finite elements, firstly deduces a formula of 6 connection modes, and utilizes programming software (Matlab) to carry out auxiliary calculation and finally carries out mechanical analysis. Compared with the existing method and model, the method can better solve the problems of multi-rigidity, non-continuity and non-linear contact of the non-continuity directional rotary steering drilling tool assembly. Has higher popularization value. The mechanical analysis time of the discontinuous directional rotary steering drilling tool combination is greatly shortened, and the cost of personnel is also reduced. The method provides a theoretical basis for the prediction of the well track and also provides a support for the structural optimization of the directional rotary steering and the evaluation of various parameters of the bottom hole assembly.

Description

Mechanical analysis method of discontinuous directional rotary steering drilling tool assembly
Technical Field
The invention relates to the field of oil and gas drilling, in particular to a mechanical analysis method of a discontinuous directional rotary steering drilling tool assembly.
Background
The directional rotary steering drilling tool represents the development trend of the current advanced drilling tool, and the discontinuous directional rotary steering drilling tool combination is more widely applied to special process wells such as ultra-deep wells, high-difficulty directional wells, cluster wells, horizontal wells, extended reach wells, branch wells and the like. Due to the high requirements on the aspects of drilling precision, well track quality, drilling speed, drilling efficiency and the like, the mechanical analysis of the discontinuous directional rotary steering drilling tool assembly is particularly important. The discontinuous directional rotary steerable drilling tool assembly comprises a drill bit, a lower stabilizer, an eccentric ring, a variable cross section, an upper stabilizer and a final contact point. The drill bit is connected with the mandrel through threads, the lower stabilizer, the variable cross section, the upper stabilizer and the final contact point are connected with the drill string through threads, and the eccentric ring is located inside the drill string and is connected with the mandrel, so that the offset is changed.
Due to the development of the intelligent drilling system, researchers at home and abroad make a great deal of research on the mechanical analysis of the discontinuous directional rotary steering drilling tool combination. In the theoretical research aspect, plum-Feng et al research the influence of factors of rotary steering on the lateral force of a drill bit, and experiments prove that the bit pressure has certain influence but is not significant on the lateral force of the drill bit. While the famous theory of the longitudinal and transverse bending method is proposed by the people of Hewlett packard and the like, the more generalized longitudinal and transverse bending method is proposed by the people of Hongdeau and the like on the basis of the theory of the longitudinal and transverse bending method, so that a model established by the original longitudinal and transverse bending method is expanded. Foreign students such as Tikhonov solve the model by considering the bending stiffness of the drill column and applying a central difference algorithm, so that the original calculation precision is improved. The Menand et al study the dynamic characteristics of the drill string by integrating the soft rod and rigid rod theories, thereby significantly improving the solving efficiency of the whole well pipe string. While in terms of finite element simulation, von willebrand et al used finite element simulation to analyze rotary steering, although finite element simulation is an approximate solution, they used finite element methods to demonstrate that bit lateral forces are also affected by well deviation. The Bulent et al scholars analyze the natural frequency of the beam by using finite elements based on the interaction mechanism of bending and torsion of the beam, and the result is consistent with the experimental result. K.K. Millheim utilizes finite element simulation to calculate the lateral force at the drill bit, and obtains that the direction of the lateral force of the drill bit is the increasing inclination when the direction of the lateral force of the drill bit is consistent with the bending direction of the well hole, otherwise, the direction of the lateral force is the decreasing inclination. Brett J.F et al performed mechanical analysis of a lower drill assembly with an elbow joint using finite element simulation. While Daily js et al studied the problem of buckling of the drill string in different boreholes by finite element analysis of the drill string in vertical, inclined, horizontal and curved wellbores as a study.
In conclusion, the limit of the longitudinal and transverse bending method can only process the problem of single variable stiffness and continuity, the method is not applicable to the problem of multiple stiffness and discontinuity, and the finite element simulation modeling is difficult to process the problem of discontinuity and nonlinear uncertain contact. Therefore, a method for solving the problems of multiple rigidity, discontinuity and nonlinear contact of the discontinuous directional rotary steerable drilling tool assembly is urgently needed.
Disclosure of Invention
The invention aims to provide the following technical scheme: aiming at the defects in the prior art, the mechanical calculation method of the discontinuous directional rotary steering drilling tool combination is provided, and compared with the existing method and model, the method can better solve the problems of multiple rigidity, discontinuity and nonlinear contact of the discontinuous directional rotary steering drilling tool combination.
The technical scheme of the invention is as follows:
a mechanical calculation method of a discontinuous directional rotary steering drilling tool assembly is characterized by comprising the following steps: the method comprises the following steps:
(1) establishing a mechanical model of the discontinuous directional rotary steering drilling tool assembly and deducing a formula through direct calculation;
the discontinuous directional rotary steering drilling tool combination is disconnected from the lower stabilizer and the upper stabilizer, the drilling tool combination between the two points can be regarded as a beam column subjected to longitudinal and transverse bending loads, and the mechanical analysis of the drilling tool combination is that the rigidity is changed due to the fact that the drilling tool combination comprises the variable cross sectionAnd (5) problems are solved. Assuming that the lower stabilizer is an R point and the upper stabilizer is a T point, and regarding the R point and the T point as two fixed hinged supports; assuming that the length between the point R and the point T is L and the unit is M, wherein the point R is subjected to a counterclockwise bending moment M1 which is expressed in the unit of N.m, and an axial load P which is in the right direction and expressed in the unit of N; the T point is subjected to a clockwise bending moment M2 with the unit of N.m and an axial load P towards the left with the unit of N; due to the variable cross section, different inertia moments and uniformly distributed loads exist on the beam column; assuming that the variable cross section is S point, the inertia moment and the uniform load at the left end are respectively I1 and q1, and the unit is m4N/m, the moment of inertia and the uniform load at the right end of the variable cross section are I2 and q2 respectively, and the units of the moment of inertia and the uniform load are m4And N/m, and I1 is less than I2, q1 is less than q 2; a micro-element section with the length of dx is taken at any position of a beam column, a plane coordinate system is established by using a point R, the micro-element section is taken for mechanical analysis, the left side of the micro-element section is assumed to be subjected to an upward section shearing force D with the unit of N, a clockwise bending moment M with the unit of N.m, a rightward axial load P with the unit of N, the right side of the micro-element section is assumed to be subjected to a downward section shearing force D + dD with the unit of N, a counterclockwise bending moment M + dM with the unit of N.m, a leftward axial load P + dP with the unit of N, and the uniform load of the micro-element section is assumed to be q with the unit of N/M. It establishes a force balance equation on the y-axis that yields:
D+dD-D+qdx＝0 (1)
taking the center of the right section of the infinitesimal section as a reference, and obtaining the center by a balance equation of moment:
Figure GDA0003462010490000031
wherein
Figure GDA0003462010490000032
Is a decimal of high order and can be ignored; from the formula of the bending moment:
Figure GDA0003462010490000033
where E is the modulus of elasticity in Pa, I is the moment of inertia in m4. The following equations (1), (2) and (3) can be obtained:
Figure GDA0003462010490000034
solving the non-homogeneous differential equation to obtain:
Figure GDA0003462010490000035
wherein C is1、C2、C3、C4Is constant, so its direct calculation formula is:
Figure GDA0003462010490000036
(2) establishing formulas of displacement, corner, bending moment and shearing force in the discontinuous directional rotary steering drilling tool assembly:
since the formula for direct calculation has been derived, the formula for its displacement is:
Figure GDA0003462010490000037
from statics knowledge, the corner θ is y ', the bending moment is M is EIy ", the shear force is F EIy'", and the corner, the bending moment and the shear force are respectively as follows:
Figure GDA0003462010490000041
Figure GDA0003462010490000042
Figure GDA0003462010490000043
(3) processing of various connection modes in non-continuous directional rotary steering drilling tool assembly
Carrying out a column equation set on various connection modes in the discontinuous directional rotary guide by using the derivation formula, the continuity condition and the boundary condition; the system of equations is then matrix transformed. In the discontinuous directional rotary guide, nodes are respectively established at a drill bit, a lower stabilizer, an eccentric ring, a variable cross section, an upper stabilizer, a final contact point and the like by utilizing the idea of unit division, wherein the drill bit is assumed to be a point A, the lower stabilizer is assumed to be a point B, a mandrel in the lower stabilizer is a point B1, the outer part of the lower stabilizer connected with a drill string is a point B2, the eccentric ring is a point C, the inner part of the eccentric ring is a point C1, the drill string at the outer side of the eccentric ring is a point C2, the variable cross section is a point D, the upper stabilizer is a point E, and the final contact point is a point F. From the drill bit, setting the point A to the point B as a first section, the point B1 to the point C1 as a second section, the point B2 to the point C2 as a third section, the point C2 to the point D as a fourth section, the point D to the point E as a fifth section, and the point E to the point F as a sixth section;
since the point A is hinged, the displacement is 0, the bending moment is 0, and the tabulatable equation system is y through the formulas (7) and (9)AB＝0、EIy’AB0, the conversion into a matrix equation is:
Figure GDA0003462010490000044
wherein
Figure GDA0003462010490000045
IiIs the moment of inertia of the i-th segment in m4，qiIs the uniform load of the ith section, and the unit is N/m, Ci1、Ci2、Ci3、Ci4For each coefficient in the equation of section i.
At the point B, because the displacements of the first section, the second section and the third section at the point are all 0, the rotation angles and the displacements of the first section and the second section at the point are also equal, and simultaneously, because the third sectionThe bending moment at this point is 0; the system of equations listed by equations (7), (8) and (9) is yAB＝0、yB1C1＝0、yB2C2＝0、y’AB＝y’B1C1、EIy”AB＝EIy”B1C1、EIy”B2C20, the conversion into a matrix equation is:
Figure GDA0003462010490000051
Figure GDA0003462010490000052
wherein liIs the length of the ith segment; the unit is m.
At the point C, because the displacement, the corner and the bending moment of the third section and the fourth section are equal at the point, the bending moment of the second section at the point is 0, the displacement of the second section is equal to the displacement of the third section minus the offset, and meanwhile, the sum of the shearing forces of the second section and the third section is equal to the shearing force of the fourth section; then the equations given by equations (7), (8), (9) and (10) can be set as yB2C2＝yCD、y’B2C2＝y’CD、EIy”B2C2＝EIy”CD、EIy”B1C1＝0、yB1C1＝yB2C2-e、EIy’”B1C1+EIy’”B2C2＝EIy’”CDThe conversion into a matrix equation is:
Figure GDA0003462010490000053
Figure GDA0003462010490000061
at the point D, because the displacement, the corner, the bending moment and the shearing force of the fourth section and the fifth section are equal at the point, the equation set which can be listed by the formulas (7), (8), (9) and (10) is yCD＝yDE、y’CD＝y’DE、EIy”CD＝EIy”DE、EIy’”CD＝EIy’”DEThe conversion into a matrix equation is:
Figure GDA0003462010490000062
at the point E, because the displacements of the fifth section and the sixth section at the point are both 0, and the turning angle and the bending moment are both equal, the equation set which can be listed by the formulas (7), (8) and (9) is yDE＝0、yEF＝0、y’EF＝y’DE、EIy”EF＝EIy”DEThe conversion into a matrix equation is:
Figure GDA0003462010490000071
at point F, since the sixth section is at this point at a rotational angle of 0, the displacement is equal to the borehole diameter minus the outer diameter of the drill pipe divided by 2, then the system of equations by equations (7), (8) is y'EF＝0、
Figure GDA0003462010490000072
The conversion into a matrix equation is:
Figure GDA0003462010490000073
wherein is d2Outside diameter of drill rod in mm, d1Is the borehole diameter. The unit is mm.
(4) Determining the length of a sixth section in the non-continuous directional rotary steering drilling tool assembly, and combining matrixes of various connection modes in the whole drilling tool assembly together to form a unified mechanical equation set of the bottom drilling tool assembly, wherein the unified mechanical equation set comprises a linear matrix equation (17) and a nonlinear equation (18);
the linear matrix equation is:
YX＝Z (17)
wherein:
Figure GDA0003462010490000074
Yidenotes the ith dot connection mode matrix, XiCoefficient matrices representing i-segment displacement functions, ZiRepresenting a constant matrix processed by an i-point connection mode;
the nonlinear equation is:
Figure GDA0003462010490000081
because only the length of the six-section in the whole rotary guide is unknown, the length of the six-section is required to be solved only by an iterative method, the length of the final section is from 0.1m, 0.1m is added for one cycle, a linear matrix equation YX is circularly calculated to be Z, then the bending moment of the final contact point in the sixth section is obtained, and if the absolute value of the bending moment is less than or equal to 10N/m, the value is taken as the length of the sixth section;
(5) programming of a discontinuous directional rotary steerable drilling assembly:
writing the formulas (7) to (18) into the software respectively through Matlab programming software, and finally, directly performing operation only by inputting known parameters of all the sections and the length of the sixth section, wherein the length of the sixth section is from 0.1 m;
(6) establishing equations of all sections in the non-continuity directional rotary steerable drilling tool assembly:
when the length of the sixth section is determined, the whole linear matrix equation is determined, and the equations from the first section to the sixth section can be solved only by once calculation, so that the sizes of the corner, the bending moment, the displacement and the shearing force are solved.
(7) Solving an integral bending moment diagram, a displacement diagram and a shear diagram:
and (4) obtaining an overall bending moment diagram, a displacement diagram and a shearing diagram by utilizing the programming software of the step (5) on the basis of the known equations of the sections of the step (6). The bending moment value and displacement of each point can be measured by the integral bending moment diagram, displacement diagram and shear diagram
And carrying out comparative analysis on the values and the magnitude of the shear force value.
The invention has the beneficial effects that:
the invention adopts the thought of a infinitesimal method and finite elements, firstly deduces a formula of 6 connection modes, and utilizes programming software (Matlab) to carry out auxiliary calculation and finally carries out mechanical analysis. Compared with the existing method and model, the method can better solve the problems of multi-rigidity, non-continuity and non-linear contact of the non-continuity directional rotary steering drilling tool assembly. Has higher popularization value. The mechanical analysis time of the discontinuous directional rotary steering drilling tool combination is greatly shortened, and the cost of personnel is also reduced. The method provides a theoretical basis for the prediction of the well track and also provides a support for the structural optimization of the directional rotary steering and the evaluation of various parameters of the bottom hole assembly.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a mechanical model of the present invention;
FIG. 3 is a schematic view of a discontinuous directional rotary steerable bottom hole assembly of the present invention;
FIG. 4 is a schematic view of specific examples enumerated in the present invention;
FIG. 5 is a schematic illustration of the resulting calculated bending moment for the embodiments recited in the present invention;
FIG. 6 is a graphical representation of the resulting displacement for the embodiments recited in the present invention;
FIG. 7 is a final calculated shear diagram for the embodiment listed in the present invention;
fig. 8 is a schematic diagram of the calculation results of each node in the embodiment listed in the present invention.
Detailed Description
The method mainly comprises the steps of establishing a mechanical model of the discontinuous directional rotary steering drilling tool assembly and deducing a formula for direct calculation; establishing formulas of displacement, corner, bending moment and shearing force in the discontinuous directional rotary steering drilling tool assembly; processing various connection modes in the discontinuous directional rotary steering drilling tool combination; determining the length of a sixth section in the non-continuous directional rotary steering drilling tool assembly; programming the discontinuous directional rotary steering drilling tool assembly; establishing equations of all sections in the discontinuous directional rotary steering drilling tool assembly; the invention is further described by the overall bending moment diagram, the displacement diagram and the shearing diagram with reference to the attached figures 1 to 8.
A mechanical analysis method of a discontinuous directional rotary steering drilling tool assembly is characterized by comprising the following steps:
(1) establishing a mechanical model of the discontinuous directional rotary steering drilling tool assembly and deducing a formula through direct calculation;
establishing a mechanical model as shown in the attached figure 2 of the specification, and disconnecting the discontinuous directional rotary steering drilling tool assembly from the lower stabilizer and the upper stabilizer, wherein the drilling tool assembly between the lower stabilizer and the upper stabilizer can be regarded as a beam column subjected to longitudinal and transverse bending loads, and the mechanical analysis of the drilling tool assembly is the variable stiffness problem because the drilling tool assembly comprises a variable cross section. Assuming that the lower stabilizer is an R point and the upper stabilizer is a T point, and regarding the R point and the T point as two fixed hinged supports; assuming that the length between the point R and the point T is L and the unit is M, wherein the point R is subjected to a counterclockwise bending moment M1 and the unit is N.m, and the unit is N; the T point is subjected to a clockwise bending moment M2 with the unit of N.m and an axial load P towards the left with the unit of N; due to the variable cross section, different inertia moments and uniformly distributed loads exist on the beam column; assuming that the variable cross section is S point, the inertia moment and the uniform load at the left end are respectively I1 and q1, and the unit is m4N/m, the moment of inertia and the uniform load at the right end of the variable cross section are I2 and q2 respectively, and the units of the moment of inertia and the uniform load are m4And N/m, and I1 is less than I2, q1 is less than q 2; taking a infinitesimal section with the length of dx at any position of a beam column, establishing a plane coordinate system by using a point R, taking the infinitesimal section for mechanical analysis, assuming that the left side of the infinitesimal section is subjected to an upward section shearing force D with the unit of N, a clockwise bending moment M with the unit of N.m, a rightward axial load P with the unit of N, and the right side of the infinitesimal section is subjected to a downward section shearing force D + dD with the unit of N, a counterclockwise bending moment M + dM with the unit of N.m, a leftward axial load P + dP with the unit of N, and setting the uniform load of the infinitesimal sectionIs q, the unit is N/m. It establishes a force balance equation on the y-axis that yields:
D+dD-D+qdx＝0 (1)
taking the center of the right section of the infinitesimal section as a reference, and obtaining the center by a balance equation of moment:
Figure GDA0003462010490000101
wherein
Figure GDA0003462010490000102
Is a decimal of high order and can be ignored; from the formula of the bending moment:
Figure GDA0003462010490000103
where E is the modulus of elasticity in Pa, I is the moment of inertia in m4. The following equations (1), (2) and (3) can be obtained:
Figure GDA0003462010490000104
solving the non-homogeneous differential equation to obtain:
Figure GDA0003462010490000105
wherein C is1、C2、C3、C4Is constant, so its direct calculation formula is:
Figure GDA0003462010490000106
(2) establishing formulas of displacement, corner, bending moment and shearing force in the discontinuous directional rotary steering drilling tool assembly:
since the formula for direct calculation has been derived, the formula for its displacement is:
Figure GDA0003462010490000111
from statics knowledge, the corner θ is y ', the bending moment is M is EIy ", the shear force is F EIy'", and the corner, the bending moment and the shear force are respectively as follows:
Figure GDA0003462010490000112
Figure GDA0003462010490000113
Figure GDA0003462010490000114
(3) processing of various connection modes in non-continuous directional rotary steering drilling tool assembly
Carrying out a column equation set on various connection modes in the discontinuous directional rotary guide by using the derivation formula, the continuity condition and the boundary condition; the system of equations is then matrix transformed. In the non-continuous directional rotary guide, nodes are respectively established at a drill bit, a lower stabilizer, an eccentric ring, a variable cross section, an upper stabilizer, a final contact point and the like by utilizing the idea of unit division, wherein the drill bit is assumed to be a point A, the lower stabilizer is assumed to be a point B, a mandrel in the lower stabilizer is the point B1, the outer part of the lower stabilizer connected with a drill string is the point B2, the eccentric ring is the point C, the inner part of the eccentric ring is the point C1, and the drill string at the outer side of the eccentric ring is the point C
Point C2, variable cross-section D, upper stabilizer E, and final contact point F. From the drill bit, a first section is set from the point A to the point B, a second section is set from the point B1 to the point C1, a third section is set from the point B2 to the point C2, a fourth section is set from the point C2 to the point D, a fifth section is set from the point D to the point E, and a sixth section is set from the point E to the point F.
See the description at point A in FIG. 3, whereAt this point, the hinge is formed, so that the displacement is 0 and the bending moment is 0, and then the tabulatable equation set is y according to the equations (7) and (9)AB＝0、EIy”AB0, the conversion into a matrix equation is:
Figure GDA0003462010490000115
wherein
Figure GDA0003462010490000116
IiIs the moment of inertia of the i-th segment in m4，qiIs the uniform load of the ith section, and the unit is N/m, Ci1、Ci2、Ci3、Ci4For each coefficient in the equation of section i.
Referring to the point B in the attached figure 3 of the specification, because the displacements of the first section, the second section and the third section at the point are all 0, the turning angles and the displacements of the first section and the second section at the point are also equal, and meanwhile, because the bending moment of the third section at the point is 0; the equations listed by the equations (7), (8) and (9) are set as
yAB＝0、yB1C1＝0、yB2C2＝0、y’AB＝y’B1C1、EIy”AB＝EIy”B1C1、EIy”B2C20, the conversion into a matrix equation is:
Figure GDA0003462010490000121
Figure GDA0003462010490000122
wherein liIs the length of the ith segment and has the unit of m.
Referring to the point C in the attached figure 3 of the specification, because the displacement, the corner and the bending moment of the third section and the fourth section are equal at the point, the bending moment of the second section at the point is 0, the displacement of the second section is equal to the displacement of the third section minus the offset, and meanwhile, the sum of the shearing forces of the second section and the third section is equal to the shearing force of the fourth sectionForce. Then the equations given by equations (7), (8), (9) and (10) can be set as yB2C2＝yCD、y’B2C2＝y’CD、EIy”B2C2＝EIy”CD、EIy”B1C1＝0、yB1C1＝yB2C2-e、EIy’”B1C1+EIy’”B2C2＝EIy’”CDConverted into a matrix equation of
Figure GDA0003462010490000131
Figure GDA0003462010490000132
Referring to the point D in the attached figure 3 of the specification, since the displacement, the corner, the bending moment and the shearing force of the fourth section and the fifth section are equal at the point, the tabulatable equation system of the formulas (7), (8), (9) and (10) is yCD＝yDE、y′CD＝y′DE、EIy”CD＝EIy”DE、EIy’”CD＝EIy’”DEConverted into a matrix equation of
Figure GDA0003462010490000133
Referring to point E in the attached figure 3 of the specification, because the displacement of the fifth section and the sixth section at the point is 0, the turning angle and the bending moment are equal, the tabulated equations of the formulas (7), (8) and (9) are yDE＝0、yEF＝0、y’EF＝y’DE、EIy”HF＝EIy”DEConverted into a matrix equation of
Figure GDA0003462010490000141
Referring to the description at point F in FIG. 3, since the sixth section has a rotation angle of 0 at this point, the displacement is equal to the borehole diameter minus the drill pipe outer diameter divided by 2, and the equations are listed in equations (7) and (8)y’EF＝0、
Figure GDA0003462010490000142
Conversion to the matrix equation of
Figure GDA0003462010490000143
Wherein d is2Is the outside diameter of the drill rod in mm, d1Is the borehole diameter. The unit is mm.
(4) The determination of the sixth section length in the non-continuous directional rotary steerable drilling assembly combines the matrices of various connections throughout the drilling assembly to form a unified mechanical equation set for the bottom hole assembly, which includes a linear matrix equation (17) and a non-linear equation (18).
The linear matrix equation is:
YX＝Z (17)
wherein:
Figure GDA0003462010490000144
Yidenotes the ith dot connection mode matrix, XiCoefficient matrices representing i-segment displacement functions, ZiRepresenting a constant matrix processed by an i-point connection mode;
the nonlinear equation is:
Figure GDA0003462010490000151
because only the length of the six sections in the whole rotary guide is unknown, the length of the rotary guide can only be solved by an iterative method,
and the length of the last segment starts from 0.1m, 0.1m is added in a cycle, a linear matrix equation YX is circularly calculated to be Z, then the bending moment of the last contact point in the sixth segment is obtained, and if the absolute value of the bending moment is less than or equal to 10N/m, the value is taken as the length of the sixth segment;
(5) programming of a discontinuous directional rotary steerable drilling assembly:
writing the formulas (7) to (18) into the software respectively through Matlab programming software, and finally, directly performing operation only by inputting known parameters of all the sections and the length of the sixth section, wherein the length of the sixth section is from 0.1 m;
(6) establishing equations of all sections in the non-continuity directional rotary steerable drilling tool assembly:
when the length of the sixth section is determined, the whole linear matrix equation is determined, and the equations from the first section to the sixth section can be solved only by once calculation, so that the sizes of the corner, the bending moment, the displacement and the shearing force are solved.
(7) Solving an integral bending moment diagram, a displacement diagram and a shear diagram:
and (5) programming software by using the step (5), and obtaining an overall bending moment diagram, a displacement diagram and a shearing diagram of the bending moment diagram, the displacement diagram and the shearing diagram on the basis of the known equation of each section in the step (6). Through the whole bending moment diagram, the displacement diagram and the shear diagram, the magnitude of the bending moment value, the displacement value and the shear value of each point can be compared and analyzed. The specific flow chart is shown in the attached figure 1 in the specification.
In order to verify the correctness of the present formula and software programming. The embodiment is verified by taking the practical example, the non-continuous directional rotary guiding example is shown in the attached figure 4 of the specification, and the specific parameters are shown in the following table
Parameter(s) Numerical value
Well angle 90°
Borehole size 215.9mm
Weight on bit 245kN
Density of drilling fluid 1.2g/cm^2
Stabilizer outer diameter 215.9mm
Density of drilling tool 7850kg/m^3
Young's modulus 2.06*10^11Pa
Circular cross section A-A Outer diameter 78mm and inner diameter 56mm
Circular cross section B-B 193mm outside diameter and 100mm inside diameter
Circular cross section C-C 193mm outside diameter and 140mm inside diameter
Circular cross section D-D 175mm outside diameter and 127mm inside diameter
In fig. 4, the zero point is taken as a two-dimensional coordinate axis at the drill bit. The offset is negative downwards. Through the calculation of MATLAB programming software, specific bending moment values (see the attached figure 5 of the specification), offset values (see the attached figure 6 of the specification) and shear values (see the attached figure 7 of the specification) of all points in the whole are obtained. Wherein each segment in the shear diagram is divided into segments in every two connection modes. Referring to the description and the attached figure 8, the displacement and bending moment of the drill bit are both zero, and the result is the same as the assumed conditions of the drill bit; secondly, when the displacement of the lower stabilizer is zero, the bending moment value is equal in the first equation and the second equation, and the bending moment value is zero in the third equation, the point is a discontinuous point, and the calculation result is the same as the assumed condition at the point; thirdly, at the eccentric ring, because the offset of the mandrel is 3mm different from that of the drill string, the displacement of the mandrel is the same as the value calculated by the bending moment in the third section of equation and the fourth section of equation, and the bending moment in the second section of equation is zero, the point is a discontinuous point, and the calculation result is the same as the assumed condition at the point; fourthly, at the variable cross section, because the calculated offset, the bending moment and the shearing force are equal to the values calculated in the fourth and fifth section equations, the calculation result is the same as the assumed condition at the point; the displacement at the upper stabilizer is zero, and the bending moment is equal in the fifth and sixth equations, so that the point is a continuous point, and the calculation result is the same as the assumed condition at the point; sixthly, at the final contact point, the calculation result is the same as the assumed condition at the point because the displacement is equal to the external diameter of the drill string minus the diameter of the borehole and divided by 2. In summary, the calculation result of the non-continuous directional rotary steering is the same as the assumed conditions of various connection modes, so that the correctness of the method is verified.
Through the whole bending moment diagram, the displacement diagram and the shear diagram, the magnitude of the bending moment value, the displacement value and the shear value of each point can be compared and analyzed.
The above description is only an example of the method of the present invention, and any simple modification or variation of the above embodiments based on the technical essence of the present invention and possible changes or modifications using the above technical content by those skilled in the art after reading the present specification still belong to the technical scope of the present invention without departing from the spirit and scope of the present invention.

Claims (1)

1. A mechanical calculation method of a discontinuous directional rotary steering drilling tool assembly is characterized by comprising the following steps: the rotary steering drilling tool assembly comprises a drill bit, a lower stabilizer, an eccentric ring and an upper stabilizer, and the mechanical calculation method comprises the following steps:
1) establishing a mechanical model of the discontinuous directional rotary steering drilling tool assembly and deducing a formula through direct calculation;
the non-continuous directional rotary steering drilling tool combination is disconnected from the lower stabilizer and the upper stabilizer, the drilling tool combination between the two points can be regarded as a beam column subjected to longitudinal and transverse bending loads, and the mechanical analysis of the drilling tool combination is a variable stiffness problem because the drilling tool combination comprises a variable cross section; assuming that the lower stabilizer is an R point and the upper stabilizer is a T point, and regarding the R point and the T point as two fixed hinged supports; assuming that the length between the point R and the point T is L and the unit is M, wherein the point R is subjected to a counterclockwise bending moment M1 and the unit is N.m, and the unit is N; the T point is subjected to a clockwise bending moment M2 with the unit of N.m and an axial load P towards the left with the unit of N; due to the variable cross section, different inertia moments and uniformly distributed loads exist on the beam column; assuming that the variable cross section is S point, the inertia moment and the uniform load at the left end are respectively I1 and q1, and the unit is m4N/m, the moment of inertia and the uniform load at the right end of the variable cross section are I2 and q2 respectively, and the units of the moment of inertia and the uniform load are m4And N/m, and I1 is less than I2, q1 is less than q 2; taking a infinitesimal section with the length of dx at any position of a beam column, establishing a plane coordinate system by using a point R, taking the infinitesimal section for mechanical analysis, assuming that the left side of the infinitesimal section is subjected to an upward section shearing force D with the unit of N, a clockwise bending moment M with the unit of N.m, a rightward axial load P with the unit of N, and the right side of the infinitesimal section is subjected to a downward section shearing force D + dD with the unit of N, a counterclockwise bending moment M + dM with the unit of N.m, a leftward axial load P + dP with the unit of N, and an evenly distributed load of the infinitesimal section of q; it establishes a force balance equation on the y-axis that yields:
D+dD-D+qdx＝0 (1)
taking the center of the right section of the infinitesimal section as a reference, and obtaining the center by a balance equation of moment:
Figure FDA0003462010480000011
wherein
Figure FDA0003462010480000012
Is a decimal of high order and can be ignored; from the formula of the bending moment:
Figure FDA0003462010480000013
where E is the modulus of elasticity in Pa, I is the moment of inertia in m4(ii) a The following equations (1), (2) and (3) can be obtained:
Figure FDA0003462010480000021
solving the non-homogeneous differential equation to obtain:
Figure FDA0003462010480000022
wherein C is1、C2、C3、C4Is constant, so its direct calculation formula is:
Figure FDA0003462010480000023
2) establishing formulas of displacement, corner, bending moment and shearing force in the discontinuous directional rotary steering drilling tool assembly:
since the formula for direct calculation has been derived, the formula for its displacement is:
Figure FDA0003462010480000024
the static knowledge shows that the rotation angle theta is y ', the bending moment is M EIy ', the shearing force is F EIy ',
then corner, bending moment, shear force are respectively:
Figure FDA0003462010480000025
Figure FDA0003462010480000026
Figure FDA0003462010480000027
3) and processing various connection modes in the discontinuous directional rotary steering drilling tool assembly:
carrying out a column equation set on various connection modes in the discontinuous directional rotary guide by using the derivation formula, the continuity condition and the boundary condition; then carrying out matrix conversion on the equation set; in the non-continuous directional rotary guide, nodes are respectively established at a drill bit, a lower stabilizer, an eccentric ring, a variable cross section, an upper stabilizer, a final contact point and the like by utilizing the idea of unit division, wherein the drill bit is assumed to be a point A, the lower stabilizer is a point B, a mandrel in the lower stabilizer is a point B1, the outer part of the lower stabilizer connected with a drill string is a point B2, the eccentric ring is a point C, the inner part of the eccentric ring is a point C1, the drill string at the outer side of the eccentric ring is a point C2, the variable cross section is a point D, the upper stabilizer is a point E, and the final contact point is a point F; from the drill bit, setting the point A to the point B as a first section, the point B1 to the point C1 as a second section, the point B2 to the point C2 as a third section, the point C2 to the point D as a fourth section, the point D to the point E as a fifth section, and the point E to the point F as a sixth section;
since the point A is hinged, the displacement is 0, the bending moment is 0, and the tabulatable equation system is y through the formulas (7) and (9)AB＝0、EIy”AB0, the conversion into a matrix equation is:
Figure FDA0003462010480000031
wherein
Figure FDA0003462010480000032
Is the moment of inertia of the i-th segment in m4Qi is the uniform load of the ith section, and the unit is N/m, Ci1、Ci2、Ci3、Ci4Calculating each coefficient in the ith section of equation;
at the point B, because the displacements of the first section, the second section and the third section at the point are all 0, the rotation angles and the displacements of the first section and the second section at the point are also equal, and simultaneously, because the bending moment of the third section at the point is 0; the system of equations listed by equations (7), (8) and (9) is yAB＝0、yB1C1＝0、yB2C2＝0、y′AB＝y′B1C1、EIy”AB＝EIy”B1C1、EIy”B2C20, the conversion into a matrix equation is:
Figure FDA0003462010480000033
Figure FDA0003462010480000041
wherein liIs the length of the ith segment and has the unit of m;
at the point C, because the displacement, the corner and the bending moment of the third section and the fourth section are equal at the point, the bending moment of the second section at the point is 0, the displacement of the second section is equal to the displacement of the third section minus the offset, and meanwhile, the sum of the shearing forces of the second section and the third section is equal to the shearing force of the fourth section; then the equations given by equations (7), (8), (9) and (10) can be set as yB2C2＝yCD、y′B2C2＝y′CD、EIy”B2C2＝EIy”CD、EIy”B1C1＝0、yB1C1＝yB2C2-e、EIy”B1C1+EIy”’B2C2＝EIy”’CDConverted into a matrix equation of
Figure FDA0003462010480000042
Figure FDA0003462010480000043
At the point D, because the displacement, the corner, the bending moment and the shearing force of the fourth section and the fifth section are equal at the point, the equation set which can be listed by the formulas (7), (8), (9) and (10) is yCD＝yDE、y’CD＝y’DE、EIy”CD＝EIy”DE、EIy”’cD＝EIy”’DEThe conversion into a matrix equation is:
Figure FDA0003462010480000051
at the point E, because the displacements of the fifth section and the sixth section at the point are both 0, and the turning angle and the bending moment are both equal, the point E is formed by the formula (7),
(8) And (9) the system of equations listed is yDE＝0、yEF＝0、y’EF＝y’DE、EIy”EF＝EIy”DEThe conversion into a matrix equation is:
Figure FDA0003462010480000052
at point F, since the sixth section turns at 0, the displacement is equal to the borehole diameter minus the drill pipe outside diameter divided by 2,
the equations listed by the equations (7) and (8) are set as
y’EF＝0、
Figure FDA0003462010480000061
The conversion into a matrix equation is:
Figure FDA0003462010480000062
wherein d is2Outside the drill rod in mm, d1Is the borehole diameter in mm;
4) and determining the length of a sixth section in the discontinuous directional rotary steerable drilling tool assembly:
combining the matrixes of various connection modes in the whole drilling tool assembly together to form a unified mechanical equation set of the bottom drilling tool assembly, wherein the unified mechanical equation set comprises a linear matrix equation (17) and a nonlinear equation (18);
the linear matrix equation is:
YX＝Z (17)
wherein:
Figure FDA0003462010480000063
Yidenotes the ith dot connection mode matrix, XiCoefficient matrices representing i-segment displacement functions, ZiRepresenting a constant matrix processed by an i-point connection mode;
the nonlinear equation is:
Figure FDA0003462010480000064
because only the length of the six-section in the whole rotary guide is unknown, the length of the six-section is required to be solved only by an iterative method, the length of the final section is from 0.1m, 0.1m is added for one cycle, a linear matrix equation YX is circularly calculated to be Z, then the bending moment of the final contact point in the sixth section is obtained, and if the absolute value of the bending moment is less than or equal to 10N/m, the value is taken as the length of the sixth section;
5) programming of the discontinuous directional rotary steerable drilling assembly:
writing the formulas (7) to (18) into the software respectively through Matlab programming software, and finally, directly performing operation only by inputting known parameters of all the sections and the length of the sixth section, wherein the length of the sixth section is from 0.1 m;
6) establishing equations of all sections in the discontinuous directional rotary steerable drilling tool assembly:
when the length of the sixth section is determined, the whole linear matrix equation is determined, and the equations from the first section to the sixth section can be solved only by once calculation, so that the sizes of a corner, a bending moment, displacement and shearing force are solved;
7) solving an integral bending moment diagram, a displacement diagram and a shear diagram:
and (4) obtaining an overall bending moment diagram, a displacement diagram and a shearing diagram by utilizing the programming software of the step (5) on the basis of the known equations of the sections of the step (6).
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