CN111428384A - Mechanical analysis method of discontinuous directional rotary steering drilling tool assembly - Google Patents
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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
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 when the direction of the lateral force of the drill bit is consistent with the bending direction of the well hole, the inclination is increased, otherwise, the inclination is decreased. 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 method comprises the steps of disconnecting a discontinuous directional rotary steering drilling tool combination from a lower stabilizer and an upper stabilizer, enabling the drilling tool combination between the two points to be regarded as a beam column subjected to longitudinal and transverse bending loads, and enabling the drilling tool combination to comprise a variable cross section, so that the mechanical analysis of the drilling tool combination is the problem of variable rigidity
N/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 are respectively
And 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 and 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 and 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:
taking the center of the right section of the infinitesimal section as a reference, and obtaining the center by a balance equation of moment:
wherein
Is a decimal of high order and can be ignored; from the formula of the bending moment:
wherein E is the modulus of elasticity in Pa, I is the moment of inertia in
. Simultaneous expression of the above formulas (1), (2), (3)
The following can be obtained:
solving the non-homogeneous differential equation to obtain:
wherein
Is constant, so its direct calculation formula is:
(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:
from statics knowledge, the turning angle is
Bending moment of
Shear force
Then corner, bending moment, shear force are respectively:
(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;
because the point A is hinged, the displacement is 0, the bending moment is 0, and the equations can be listed as formula (7) and (9)
The conversion into a matrix equation is:
wherein
，
Is the moment of inertia of the i-th segment in
，
Is the uniform load of the ith section, the unit of the uniform load is N/m,
for 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 bending moment of the third section at the point is 0; the equations listed by the equations (7), (8) and (9) are set as
The conversion into a matrix equation is:
wherein
Is 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 following equations can be obtained from equations (7), (8), (9), (10):
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 equations (7), (8), (9) and (10) can be listed as
（
、
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 can be listed as
（
) The conversion into a matrix equation is:
at point F, since the angle of rotation of the sixth section is 0 at this point, the displacement is equal to the borehole diameter minus the outer diameter of the drill pipe divided by 2, and the equations set by equations (7), (8) are given by (C:)
) The conversion into a matrix equation is:
wherein
Is the outside diameter of the drill rod, in mm,
is the borehole diameter. The unit is mm.
(4) Determination of sixth section length in non-continuous 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:
AX=Z（17）
wherein:
the nonlinear equation is:
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 AX = B is calculated in a cycle mode, 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:
respectively writing the formulas (7) to (18) into the software through Matlab programming software, and finally, directly performing operation only by inputting known parameters of all the sections and the length of a sixth section (starting 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 ① a mechanical model of the discontinuous directional rotary steering drilling tool combination and deriving a direct calculation formula, establishing ② formulas of displacement, corner, bending moment and shearing force in the discontinuous directional rotary steering drilling tool combination, processing ③ various connection modes in the discontinuous directional rotary steering drilling tool combination, determining ④ a sixth section length in the discontinuous directional rotary steering drilling tool combination, programming ⑤ the discontinuous directional rotary steering drilling tool combination, establishing ⑥ equations of each section in the discontinuous directional rotary steering drilling tool combination, and solving ⑦ an integral bending moment diagram, a displacement diagram and a shear diagram of the discontinuous directional rotary steering drilling tool combination, wherein the method is further described by combining the attached drawings 1-8.
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;
a mechanical model shown in an attached figure 2 of the specification is established, a discontinuous directional rotary steering drilling tool combination is disconnected from a lower stabilizer and an 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 drilling tool combination comprises a variable cross section, so that the mechanical analysis of the drilling tool combination is a variable stiffness problem
N/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 are respectively
And 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 and 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 and 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:
taking the center of the right section of the infinitesimal section as a reference, and obtaining the center by a balance equation of moment:
wherein
Is a decimal of high order and can be ignored; from the formula of the bending moment:
wherein E is the modulus of elasticity in Pa, I is the moment of inertia in
. The following equations (1), (2) and (3) can be obtained:
solving the non-homogeneous differential equation to obtain:
wherein
Is constant, so its direct calculation formula is:
(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:
from statics knowledge, the turning angle is
Bending moment of
Shear force
Then corner, bending moment, shear force are respectively:
(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.
Referring to the point A in the attached figure 3 of the specification, since the point is hinged, the displacement is 0, the bending moment is 0, and the equations (7), (9) can be listed as
The conversion into a matrix equation is:
wherein
，
Is the moment of inertia of the i-th segment in
，
Is the uniform load of the ith section, the unit of the uniform load is N/m,
for 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
wherein
Is 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 force of the second section and the third section is equal to the shearing force of the fourth section. Then the following equations can be obtained from equations (7), (8), (9), (10):
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 equations listed by the formulas (7), (8), (9) and (10) are set as
（
、
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, and the corner and the bending moment are equal, the equations listed by the formulas (7), (8) and (9) are set as
（
、
) Converted into a matrix equation of
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)
，
Conversion to the matrix equation of
Wherein
Is the outside diameter of the drill rod, in mm,
is the borehole diameter. The unit is mm.
(4) Determination of sixth section length in non-continuous directional rotary steerable drilling tool assembly
Combining the matrices of the various connections throughout the drill assembly together forms a unified set of mechanical equations for the bottom hole assembly, including a linear matrix equation (17) and a non-linear equation (18).
The linear matrix equation is:
AX=Z（17）
wherein:
the nonlinear equation is:
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 once, a linear matrix equation AX = B is calculated in a cycle, 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:
respectively writing the formulas (7) to (18) into the software through Matlab programming software, and finally, directly performing operation only by inputting known parameters of all the sections and the length of a sixth section (starting 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
In FIG. 4, the zero point on the two-dimensional axis at the drill bit, the offset downward, the shear force values (see FIG. 7 in the description), and the specific bending moment values at each point in the overall system (see FIG. 5 in the description), the offset values (see FIG. 6 in the description), and the shear force values (see FIG. 7 in the description) are calculated by the MAT L AB programming software, wherein each section in the shear force diagram is divided into sections at every two connections, as can be seen from FIG. 8 in the description, ① is the same as the assumed conditions at the drill bit due to zero displacement and bending moment values of the drill bit, ② is zero at the lower stabilizer with equal bending moment values in the first and second section equations, and is zero at the third section equation, which is a non-continuous point, which is the same as the assumed conditions at that point, ③ is the same as the offset of the mandrel at the eccentric ring and the offset of the bending moment calculated in the third and fourth section equations, and is the same as the assumed conditions at the second section equation, which is the same as the offset of the drill string at the third and the fourth section equation, which is the non-continuous point, which is the same as the calculated as the bending moment value at the non-continuous point, which is the calculated as the calculated at the fourth section equation, which is the calculated as the assumed conditions at the fourth section equation, which is equal to the calculated at the fifth section equation, which is equal to the calculated at the calculated as the calculated at the non-continuous point, which is equal to the calculated at the non-continuous point of the shear force point of the calculated at the third and the third section equation, which is equal to the non-continuous equation, which is the.
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 method comprises the steps of disconnecting a discontinuous directional rotary steering drilling tool combination from a lower stabilizer and an upper stabilizer, enabling the drilling tool combination between the two points to be regarded as a beam column subjected to longitudinal and transverse bending loads, enabling the drilling tool combination to comprise a variable cross section, enabling mechanical analysis of the drilling tool combination to be a stiffness problem, enabling the lower stabilizer to be a point R and the upper stabilizer to be a point T, enabling the point R and the point T to be regarded as two fixed hinged supports, enabling the length between the point R and the point T to be L in M, enabling the point R to be subjected to a counterclockwise bending moment M1 in an N ∙ M and an axial load P in a right direction in an N, enabling the point T to be subjected to a clockwise bending moment M2 in an N ∙ M and an axial load P in a left direction in an N, enabling different moments of inertia and uniform loads to exist on the beam column due to the variable cross section, enabling the moment of the left end and the uniform loads to be I1 and q1 in an S point respectively in an S cross section
N/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 are respectively
And N/m, and I1 is less than I2, q1 is less than q 2; taking a micro-element 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 micro-element section for mechanical analysis, and assuming that the left side of the micro-element section is subjected to an upward section shearing force D, the unit of the shear force D is N, a clockwise bending moment M, the unit of the bending moment M is N ∙ M, and a rightward axial load P, the unit of the bending moment M is N, and the right side of the micro-element section is subjected to a rightward axial load P, the unit of the axial loadThe unit of the lower section shearing force D + dD is N, the unit of the bending moment M + dM in the anticlockwise direction is N ∙ M, the unit of the axial load P + dP in the left direction is N, and the unit of the uniform load of the infinitesimal section is q; it establishes a force balance equation on the y-axis that yields:
taking the center of the right section of the infinitesimal section as a reference, and obtaining the center by a balance equation of moment:
wherein
Is a decimal of high order and can be ignored; from the formula of the bending moment:
wherein E is the modulus of elasticity in Pa, I is the moment of inertia in
(ii) a The following equations (1), (2) and (3) can be obtained:
solving the non-homogeneous differential equation to obtain:
wherein
Is constant, so its direct calculation formula is:
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:
from statics knowledge, the turning angle is
Bending moment of
Shear force
Then corner, bending moment, shear force are respectively:
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;
because the point A is hinged, the displacement is 0, the bending moment is 0, and the equations can be listed as formula (7) and (9)
The conversion into a matrix equation is:
wherein
Is the moment of inertia of the i-th segment in
Qi is the uniform load of the ith section, and the unit is N/m,
calculating 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 equations listed by the equations (7), (8) and (9) are set as
Is converted into momentThe array equation is:
wherein
Is 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 the sum of the shearing force of the second section and the third section is equal to the shearing force of the fourth section, the equations (7), (8), (9) and (10) can be listed as follows:
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 equations (7), (8), (9) and (10) can be listed as
、
The conversion into a matrix equation is:
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 can be listed as
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
wherein
Is outside the drill rod, the unit is mm,
is 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:
AX=B（17）
wherein:
the nonlinear equation is:
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 AX = B is calculated in a cycle mode, 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:
respectively writing the formulas (7) to (18) into the software through Matlab programming software, and finally, directly performing operation only by inputting known parameters of all the sections and the length of a sixth section (starting 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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| US20080230272A1 (en) * | 2006-07-21 | 2008-09-25 | Halliburton Energy Services, Inc. | Method and System for Designing Bottom Hole Assembly Configuration |
| CN102063541A (en) * | 2010-12-30 | 2011-05-18 | 中国海洋石油总公司 | Multi-body dynamic quick analysis modeling method for rotary steering drilling system |
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