CN111428385B - Mechanical analysis method of push-type rotary steering drilling tool assembly - Google Patents
Mechanical analysis method of push-type rotary steering drilling tool assembly Download PDFInfo
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- 238000005553 drilling Methods 0.000 title claims abstract description 248
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Abstract
The invention belongs to the technical field of petroleum drilling tools, and particularly relates to a mechanical analysis method of a push-type rotary steering drilling tool assembly. According to the invention, when a mechanical model is established for the push-pull type rotary steering drilling tool combination, the problem of a plurality of different rigidities among drill strings is considered, and infinite push-pull type rotary steering drilling tool combinations with a plurality of rigidities can be processed according to a real situation, so that an analysis result is closer to the real situation. 1. A mechanical analysis model of the push-pull type rotary steering drilling tool combination is established by utilizing a infinitesimal method and a continuous beam theory, a deformation equation of the drilling tool combination can be solved, and a corresponding displacement curve, a corner curve, a bending moment curve and a corresponding shear force curve are obtained. 2. Analyzing the influence rules of different factors on the lateral force of the drill bit of the push-pull type rotary steering drilling tool combination, and optimally designing the structural parameters of the push-pull type rotary steering drilling tool combination according to the obtained rules to improve the lateral force of the drill bit of the push-pull type rotary steering drilling tool combination. The invention can be widely applied to the field of oil and gas fields and coal bed gas development.
Description
Technical Field
The invention belongs to the technical field of petroleum drilling tools, and particularly relates to a mechanical analysis method of a push-type rotary steering drilling tool assembly.
Background
In the directional drilling process, the push-type rotary steering drilling tool assembly can conveniently adjust well deviation and orientation under the rotation state of a drilling column, and completes drilling work such as directional deviation making, deviation increasing, deviation stabilizing and the like, so that the efficiency and safety of directional drilling are greatly improved, the track control precision of a well hole is high, and the push-type rotary steering drilling tool assembly is widely applied to complex drilling processes such as directional wells, horizontal branch wells and the like.
The stress and deformation analysis of the push-pull type rotary steering drilling tool assembly is an important theoretical basis for optimizing the structural design of the push-pull type rotary steering drilling tool assembly and selecting drilling process parameters, and has very important significance for evaluating the mechanical characteristics of the push-pull type rotary steering drilling tool assembly, controlling the well track, improving the build-up rate and the like. In order to optimize parameters, improve the deflecting capability of the push-pull type rotary steering drilling tool assembly and realize accurate control of a well track, it is necessary to establish a mechanical model of the push-pull type rotary steering drilling tool assembly.
In the long-term development process of mechanical analysis of push-type rotary steerable drilling tool assemblies, a plurality of simplified models and solution methods have been established by a plurality of scholars. Lubinski et al scholars establish a third order ordinary differential equation of static analysis of a bottom hole drilling tool according to the balance condition of the drilling tool after bending deformation, and perform mechanical analysis on the drilling tool in a two-dimensional borehole with well deviation. The scholars such as the Baijia nationality simplify the bottom drilling tool assembly into an interactive elastic continuous beam, study the two-dimensional force and three-dimensional statics problems of the bottom drilling tool, and provide a longitudinal and transverse bending method. By combining the finite element division thought and the longitudinal and transverse bending method beam theory, the Hongdai and other scholars propose a generalized longitudinal and transverse bending method to carry out three-dimensional mechanical analysis on the bottom drilling tool assembly. The scholars such as brave and summer adults consider the variable stiffness problem, simplify the single-bent screw drilling tool combination into a beam column subjected to longitudinal and transverse bending loads for stress analysis, and establish a mechanical model of the single-bent screw drilling tool combination. Scholars such as Sterculia scholaris adopt a new equivalent processing method for a guide wing rib of a rotary guide system, and establish a mechanical model of a lower drilling tool assembly according to a longitudinal and transverse bending beam theory. On the basis of the equilibrium curvature method, the Zhang-Hai scholars consider the stratum well-to-well slant force and establish a calculation model considering the stratum action build-up rate. The Liu Jiangxin and other scholars establish a statics analysis model of a bottom drilling tool combination of the combined type rotary steering drilling tool through a finite element method.
These researchers have proposed many mechanical models and methods, but at most can only deal with the problem of two rigidities in one unit, and the push-type rotary steering drilling assembly generally consists of a drill bit, a rotary steering tool, stabilizers, flexible joints and drill collars, wherein the number of variable cross sections between drill strings is more than two, so the mechanical models and methods proposed by the researchers cannot well solve the problem of mechanical modeling with more than two variable cross sections between two stabilizers, and generally can only be analyzed by simplified processing, but larger errors are generated.
Based on the problems, the invention comprehensively considers various influence factors such as drilling parameters (bit pressure), drilling tool combination structure parameters (multiple variable cross sections, a stabilizer, the diameter and the position of a flexible short section and the like) and the like to establish a mechanical model of the push-pull type rotary steering drilling tool combination so as to solve the multi-section problem of the push-pull type rotary steering drilling tool combination, so that the multi-section problem of the push-pull type rotary steering drilling tool combination can be solved, the drilling tool combination with multiple rigidities can be processed according to the real situation, the analysis result is closer to the real situation, and the invention has important significance for analyzing the mechanical analysis of the push-pull type rotary steering drilling tool combination.
Disclosure of Invention
The invention aims to: the mechanical analysis method can solve the problem that the conventional mechanical model and method cannot solve the problem of variable cross sections of the push-type rotary steering drilling tool assembly.
The technical scheme of the invention is as follows:
a mechanical analysis method of a push-pull type rotary steering drilling tool assembly is characterized by comprising the following steps: the method comprises the following steps:
(1) reasonably simplifying and equivalently processing the push-type rotary steering drilling tool assembly;
the deformation of the push-type rotary steering drilling tool combination comprising a drill bit, a rotary steering tool, a stabilizer, a flexible joint and a drill collar is assumed to be small elastic deformation; the diameter of the well hole is the diameter of the drill bit, and the well wall is a rigid body; the top end of the push-type rotary guide drilling tool assembly is tangent to the wall of the lower well under the influence of self weight, and the torsional deformation of the top end is not considered; due to the influence of the self weight of the drill string, the drill string above the tangent point of the tail end of the push-type rotary steering drilling tool assembly and the well wall is laid on the lower well wall; the contact form of the push-against type rotary steering drilling tool assembly and the well wall is a point contact form; the axis of the push-type rotary steering drilling tool assembly before deformation is the axis of the well bore, and an annular gap exists between the well walls; the stabilizer is simplified and processed into a drill rod with the center point contacting with the well wall and the rest being normal drill rods; the rib position is approximately regarded as a stabilizer with certain displacement; defining a drill bit, a variable cross section, a stabilizer and a tangent point of the push-pull type rotary steering drilling tool assembly as the node position of the push-pull type rotary steering drilling tool assembly, and defining a section of drill column between the nodes;
(2) carrying out stress analysis on the pushing type rotary steering drilling tool assembly micro element section to obtain a displacement deformation equation;
taking a infinitesimal section with the length dx at any position of the push-pull type rotary steering drilling tool assembly, and carrying out stress analysis on the infinitesimal section, wherein P is an axial load and N; m is a section bending moment, N.m; q is a section shear force, N; q is uniformly distributed load, N/m; x is the length of the drill string, m; y is the displacement deformation of the drill string, m; e is the elastic modulus of the drill string material, Pa; i is the moment of inertia of the cross section, m4(ii) a The force balance equation of the infinitesimal body is formula (1):
the equation of bending moment and curvature is formula (2):
the following formulas (1) and (2) are combined:
solving the displacement deformation equation of the infinitesimal section drill string by the equation (3) as follows:
order to
The deformation equation of displacement of the infinitesimal section drill string becomes:
in formula (5): unknown constant C1、C2、C3、C4The coefficient of the infinitesimal section drill column displacement deformation equation is obtained;
(3) obtaining a corner equation, a bending moment equation and a shear force equation according to the displacement deformation equation;
any section in the push type rotary steering drilling tool assembly is defined as a first derivative, a second derivative and a third derivative of x by a displacement deformation equation of an ith section of a drill string of the push type rotary steering drilling tool assembly:
yi″′＝ki 3Ci3sin(kixi)-ki 3Ci4cos(kixi)#(9)
the displacement of the drill string is y, the cutting angle is y ', the bending moment is M which is EIy ', and the shearing force is F which is EIy ';
the equation system composed of the formula (6), the formula (7), the formula (8) and the formula (9) has the form of matrix multiplication:
(4) obtaining a matrix equation of simultaneous displacement deformation equations of two adjacent sections of drill strings of the push type rotary steering drilling tool assembly according to the step (3);
any section of the push type rotary steering drilling tool assembly is defined as the ith section of the push type rotary steering drilling tool assembly, the drill column and the next section adjacent to the drill column are defined as the jth section of the push type rotary steering drilling tool assembly, the displacement matrix equation of the ith section of the push type rotary steering drilling tool assembly and the displacement matrix equation of the jth section of the drill column are subtracted, and the matrix equation formed by the simultaneous displacement deformation equations of the two adjacent sections of the push type rotary steering drilling tool assembly is obtained as follows:
(5) determining a boundary condition and a continuity condition;
the connection mode of the node positions related to the push-type rotary steering drilling tool combination is divided into the following modes: a hinged connection mode, a variable cross-section connection mode, a stabilizer connection mode and a tangent connection mode; respectively describing boundary conditions and continuity conditions of different connection modes;
a. hinged connection (drill bit, only one section of drill string is related)
The drill bit of the push-type rotary steering drilling tool combination is hinged, the displacement y is 0, the bending moment EIy' is 0,
the boundary conditions are:
when formula (12) is taken into formula (11):
b. variable cross-section connection (drill string variable cross-section, relating two drill strings)
At the variable cross section between any two adjacent sections of drill columns of the push-type rotary steering drilling tool assembly, the displacement, the corner, the bending moment and the shearing force of the two sections of drill columns at the variable cross section are equal, and then the boundary conditions and the continuity conditions are as follows:
when formula (14) is taken into formula (11):
c. stabilizer connection mode (stabilizer between two drill columns contacting with well wall, associated two drill columns)
At the stabilizer of the push-type rotary steering drilling tool assembly, the displacement, the corner, the bending moment and the shearing force of the left and the right drill strings at the stabilizer are equal, and the displacement at the stabilizer is equal to half of the difference value between the diameter of the borehole and the outer diameter of the stabilizer, so that the boundary conditions and the continuity conditions are as follows:
when formula (16) is taken into formula (11):
d. tangent connection mode (tangent point and well wall tangent point, associated with a section of drill string)
The final section of the push-type rotary steering drilling tool assembly is at a tangent point tangent with the well wall, the rotating angle of the final section of the drill string at the tangent point is 0, the displacement is equal to half of the difference value between the diameter of the well and the outer diameter of the drill string, and the boundary condition and the continuity condition are as follows:
when formula (18) is introduced into formula (11):
formula (12) to formula (19): l isiThe length of the section i of the drill string of the push-pull type rotary steering drilling tool assembly is m; diThe outer diameter m of the ith section of a drill string of the push-pull rotary steering drilling tool assembly; d1Is the borehole diameter, m.
(6) Dividing the drilling tool assembly into units, inputting parameters and selecting a connection mode.
Dividing the push-type rotary steering drilling tool assembly into a plurality of sections of drilling strings according to the node positions, and setting the total number of the sections of the drilling strings divided by the push-type rotary steering drilling tool assembly as N; determining a connection mode of the push-pull type rotary steering drilling tool assembly according to the N +1 node positions of the push-pull type rotary steering drilling tool assembly obtained in the step (5), and substituting the bit pressure parameters of the push-pull type rotary steering drilling tool assembly and related parameters of N sections of drill strings (including the section length of the front N-1 sections of drill strings and the outer diameter, the inner diameter, the elastic modulus and the uniformly distributed load of the N sections of drill strings) into the boundary condition and the continuity condition equation of the node positions in the step (5);
(7) setting the section length range of the last section of the drill string of the push type rotary steering drilling tool assembly; the tail end of the last section of the push type rotary steering drilling tool assembly is contacted with the well wall, but the tangent point position of the contact is the section length L of the Nth section of the drill stringnAnd is uncertain in practice; the bending moment value M according to the position of the tangent point is determined, M is 0 in the horizontal well, M is EIK in the inclined well, and the K value is related to the inclination angle; therefore, it is assumed that the bending moment M at the tangent point of the nth drill string is equal to the length L of the drill string segment of EIKnBetween Lmin and Lmax. To find a drill string section length L that enables M to EIKnTo make the drill string section long LnStarting from Lmin and increasing to Lmax, finding L that can make M equal to EIKnThe value is obtained.
(8) For the push-pull type rotary steering drilling tool assembly divided into N sections, according to the boundary conditions and continuity condition equations of N +1 node positions obtained in the steps 6) and 7), 4N equation sets containing 4N unknown numbers can be obtained by performing matrix splicing according to the node positions, and a linear matrix equation AX ═ B is formed through a mechanical model as follows:
in formula (20): a. the0Is a 2 x 4 matrix, which is a boundary condition coefficient matrix at the drill bit; a. thei＝(Ai1|Ai2) A 4 × 8 matrix (i ═ 1,2, …, N-1), which is a boundary condition coefficient matrix at the end of the ith segment; a. theNIs a 2 x 4 matrix and is a boundary condition coefficient matrix at the end tangent point of the last segment. Xi＝[Ci1，Ci2，Ci3，Ci4]' is a 4 x 1 matrix, representing the unknown matrix of the i-th segment of the displacement function. B is0Is a 2 x 1 matrix, which is a matrix of boundary condition constants at the drill bit; b isiA 4 × 1 matrix (i ═ 1,2, …, N-1) is a boundary condition constant matrix at the end of the ith segment; b isNThe matrix is a 2 x 1 matrix and is a constant matrix of boundary conditions at the tangent point of the last segment.
(9) And (3) solving a matrix equation to obtain 4N unknowns of the matrix equation, wherein the 4N-3 to 4N unknowns are coefficients of the displacement deformation equation of the ith section of the drill string, so that the displacement deformation equations of the 1 st section to the Nth section of the drill string can be determined, and the rotation angle equation, the bending moment equation and the shear force equation of the 1 st section to the Nth section of the drill string can be obtained by derivation.
(10) Judging whether the bending moment value of the tail end of the last section of the push type rotary steering drilling tool assembly meets the requirement M-EIK, if yes, performing step 11, otherwise, reducing the range of the tangent length of the last section of the drilling tool assembly, and returning to step 8;
(11) obtaining equations of all units of the rotary steering drilling tool assembly and displacement curves, corner curves, bending moment curves and shear force curves of the rotary steering drilling tool assembly; judging that the bending moment value of the tail end of the last section of the push type rotary steering drilling tool combination meets the requirement M, namely EIK, and respectively sorting the bending moment value of the last section of the push type rotary steering drilling tool combination into piecewise functions according to the displacement equation, the corner equation, the bending moment equation and the shear equation of the 1 st section to the Nth section of the drill string, so that the displacement equation, the corner equation, the bending moment equation and the shear equation of the whole push type rotary steering drilling tool combination can be obtained; the displacement value of each point in the push-type rotary steering drilling tool combination is equal to the specific value of the displacement equation of the section, the turning angle value is equal to the first derivative of the turning angle equation of the section, the bending moment value is equal to the second derivative of the bending moment equation of the section and then multiplied by EI, and the shearing force value of each point is equal to the third derivative of the shearing force equation of the section and then multiplied by EI, so that a displacement function curve, a turning angle function curve, a bending moment function curve and a shearing force function curve of the whole push-type rotary steering drilling tool combination are obtained, and the displacement curve, the turning angle curve, the bending moment curve and the shearing force curve of the push-type rotary steering drilling tool combination can be obtained by drawing the function curves in MATLAB drawing software.
The invention has the advantages that:
according to the invention, when a mechanical model is established for the push-pull type rotary steering drilling tool combination, the problem of a plurality of different rigidities among drill strings is considered, and infinite push-pull type rotary steering drilling tool combinations with a plurality of rigidities can be processed according to a real situation, so that an analysis result is closer to the real situation. 1. A mechanical analysis model of the push-pull type rotary steering drilling tool combination is established by utilizing a infinitesimal method and a continuous beam theory, a deformation equation of the drilling tool combination can be solved, and a corresponding displacement curve, a corner curve, a bending moment curve and a corresponding shear force curve are obtained. 2. Analyzing the influence rules of different factors on the lateral force of the drill bit of the push-pull type rotary steering drilling tool combination, and optimally designing the structural parameters of the push-pull type rotary steering drilling tool combination according to the obtained rules to improve the lateral force of the drill bit of the push-pull type rotary steering drilling tool combination. The invention can be widely applied to the field of oil and gas fields and coal bed gas development.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a force analysis diagram of the micro-elements of the push-against type rotary steerable drilling assembly of the present invention;
FIG. 3 is a schematic view of a static push-against rotary steerable drilling assembly of the present invention;
FIG. 4 is a schematic view of a drilling assembly according to a first embodiment of the present invention;
FIG. 5 is a final calculated overall displacement map of the drilling assembly in accordance with an embodiment of the present invention;
FIG. 6 is a flow chart illustrating mechanical analysis of a drilling assembly according to the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
The invention provides a mechanical analysis method of a push-type rotary steering drilling tool assembly, which comprises the following steps (see the attached drawing 1 in the specification):
(1) reasonably simplifying and equivalently processing the push-type rotary steering drilling tool assembly;
the deformation of the push-type rotary steering drilling tool combination comprising a drill bit, a rotary steering tool, a stabilizer, a flexible joint and a drill collar is assumed to be small elastic deformation; the diameter of the well hole is the diameter of the drill bit, and the well wall is a rigid body; the top end of the push-type rotary guide drilling tool assembly is tangent to the wall of the lower well under the influence of self weight, and the torsional deformation of the top end is not considered; due to the influence of the self weight of the drill string, the drill string above the tangent point of the tail end of the push-type rotary steering drilling tool assembly and the well wall is laid on the lower well wall; the contact form of the push-against type rotary steering drilling tool assembly and the well wall is a point contact form; the axis of the push-type rotary steering drilling tool assembly before deformation is the axis of the well bore, and an annular gap exists between the well walls; the stabilizer is simplified and processed into a drill rod with the center point contacting with the well wall and the rest being normal drill rods; the rib position is approximately regarded as a stabilizer with certain displacement; and defining the positions of a drill bit, a variable cross section, a stabilizer and a tangent point of the push-pull type rotary steering drilling tool assembly as the positions of nodes of the push-pull type rotary steering drilling tool assembly, and defining a section of drill string between the nodes.
(2) Carrying out stress analysis on the pushing type rotary steering drilling tool assembly micro element section to obtain a displacement deformation equation; taking a infinitesimal section with the length dx at any position of the push-pull type rotary steering drilling tool assembly, and carrying out stress analysis on the infinitesimal section, wherein the figure 2 in the specification is shown, P is axial load, and N is axial load; m is a section bending moment, N.m; q is a section shear force, N; q is uniformly distributed load, N/m; x is the length of the drill string, m; y is the displacement deformation of the drill string, m; e is the elastic modulus of the drill string material, Pa; i is the moment of inertia of the cross section, m4。
The force balance equation of the infinitesimal body is formula (1):
the equation of bending moment and curvature is formula (2):
the following formulas (1) and (2) are combined:
solving the displacement deformation equation of the infinitesimal section drill string by the equation (3) as follows:
order to
The deformation equation of displacement of the infinitesimal section drill string becomes:
in formula (5): unknown constant C1、C2、C3、C4The coefficient of the infinitesimal section drill string displacement deformation equation is obtained.
(3) Obtaining a corner equation, a bending moment equation and a shear force equation according to the displacement deformation equation;
the displacement deformation equation of any section (defined as the ith section of the push type rotary steering drilling tool assembly) of the drill string in the push type rotary steering drilling tool assembly calculates the first derivative, the second derivative and the third derivative of x:
yi″′＝ki 3Ci3sin(kixi)-ki 3Ci4cos(kixi)#(9)
the displacement of the drill string is y, the tangent angle is y ', the bending moment is M-EIy ', and the shearing force is F-EIy '.
The equation system composed of the formula (6), the formula (7), the formula (8) and the formula (9) has the form of matrix multiplication:
(4) obtaining a matrix equation of simultaneous displacement deformation equations of two adjacent sections of drill strings of the push type rotary steering drilling tool assembly according to the step (3);
any section of the push type rotary steering drilling tool assembly is defined as the ith section of the drill string of the push type rotary steering drilling tool assembly, the next section adjacent to the ith section is defined as the jth section of the push type rotary steering drilling tool assembly, and the displacement matrix equation of the ith section of the drill string and the jth section of the drill string are subtracted to obtain the matrix equation of the displacement deformation equation simultaneous of the adjacent sections of the drill string of the push type rotary steering drilling tool assembly as follows:
(5) determining a boundary condition and a continuity condition;
for a certain node, generally, one node is associated with two sections of drill strings; in special cases, the drill bit node and the borehole wall contact node are associated with only one drill string section, but can be derived from two drill string sections when deriving the formula.
The connection mode of the node positions related to the push-type rotary steering drilling tool combination is divided into the following modes: a hinged connection mode, a variable cross-section connection mode, a stabilizer connection mode and a tangent connection mode. Taking the static push-against type rotary guide drilling tool assembly as an example in fig. 3, boundary conditions and continuity conditions are respectively described for different connection modes.
a. Hinged connection (drill bit, only one section of drill string is related)
If the point a of the push-type rotary steerable drilling assembly in fig. 3 is hinged, the displacement y is 0 and the bending moment EIy "is 0, the boundary conditions are as follows:
when formula (12) is taken into formula (11):
b. variable cross-section connection (drill string variable cross-section, relating two drill strings)
In the variable cross section between any two adjacent sections of drill columns of the push-type rotary steering drilling tool assembly, such as point B, point C, point E, point F and point H in fig. 3, the displacement, the corner, the bending moment and the shearing force of the two sections of drill columns at the variable cross section are equal, and then the boundary conditions and the continuity conditions are as follows:
when formula (14) is taken into formula (11):
c. stabilizer connection mode (stabilizer between two drill columns contacting with well wall, associated two drill columns)
At the stabilizer of the push-type rotary steering drilling tool assembly, as shown at points D and G in fig. 3, the displacement, the rotation angle, the bending moment and the shearing force of the two sections of drill strings at the left and right of the stabilizer are equal, and the displacement at the stabilizer is equal to half of the difference between the diameter of the borehole and the outer diameter of the stabilizer, so the boundary conditions and the continuity conditions are as follows:
when formula (16) is taken into formula (11):
d. tangent connection mode (tangent point and well wall tangent point, associated with a section of drill string)
The tangent point of the last section of the push-against type rotary steering drilling tool assembly tangent with the well wall, such as the tangent point K in fig. 3, the corner of the last section of the drill string at the tangent point is 0, the displacement is equal to half of the difference between the diameter of the well and the outer diameter of the drill string, and then the boundary condition and the continuity condition are as follows:
when formula (18) is introduced into formula (11):
formula (12) to formula (19): l isiThe length of the section i of the drill string of the push-pull type rotary steering drilling tool assembly is m; diFor pushing against type rotary steering drill stringThe outer diameter, m, of the combined i-th section of the drill string; d1Is the borehole diameter, m.
(6) Dividing the drilling tool assembly into units, inputting parameters and selecting a connection mode.
Dividing the push-type rotary steering drilling tool assembly into a plurality of sections of drilling strings according to the node positions, and setting the total number of the sections of the drilling strings divided by the push-type rotary steering drilling tool assembly as N. And (4) determining the connection mode of the N +1 node positions of the push-pull type rotary steering drilling tool assembly according to the positions obtained in the step (5), and substituting the bit pressure parameters of the push-pull type rotary steering drilling tool assembly and the related parameters of the N sections of drill strings (including the section length of the front N-1 sections of drill strings and the outer diameter, the inner diameter, the elastic modulus and the uniformly distributed load of the N sections of drill strings) into the boundary condition and the continuity condition equation of the node positions in the step (5).
(7) The range of the length of the last drill string section of the push-against rotary steerable drilling assembly is given.
The end of the last drill string of the push-against rotary steerable drilling assembly is in contact with the borehole wall, but the location of the tangent point of contact (i.e., the length Ln of the nth drill string) is practically uncertain. The bending moment value M according to the tangent point position is determined (M is 0 in a horizontal well, and M is EIK in an inclined well (the K value is related to the well inclination angle)), so that the drill string section length Ln of the N section of drill string with the bending moment value M being EIK is between Lmin and Lmax. To find the drill string section length Ln that specifically enables M to EIK, the drill string section length Ln is incremented from Lmin to Lmax, finding the Ln value that enables M to EIK.
(8) For the push-pull type rotary steering drilling tool assembly divided into N sections, according to the boundary conditions and continuity condition equations of the N +1 node positions obtained in the steps (6) and (7), 4N equation sets containing 4N unknown numbers can be obtained by performing matrix splicing according to the node positions, and a linear matrix equation AX ═ B is formed through a mechanical model as follows:
in formula (20): a. the0Is a 2 x 4 matrix, which is a boundary condition coefficient matrix at the drill bit; a. thei＝(Ai1|Ai2) A 4 × 8 matrix (i ═ 1,2, …, N-1), which is a boundary condition coefficient matrix at the end of the ith segment; a. theNIs a 2 x 4 matrix and is a boundary condition coefficient matrix at the end tangent point of the last segment. Xi＝[Ci1，Ci2，Ci3，Ci4]' is a 4 x 1 matrix, representing the unknown matrix of the i-th segment of the displacement function. B is0Is a 2 x 1 matrix, which is a matrix of boundary condition constants at the drill bit; b isiA 4 × 1 matrix (i ═ 1,2, …, N-1) is a boundary condition constant matrix at the end of the ith segment; b isNThe matrix is a 2 x 1 matrix and is a constant matrix of boundary conditions at the tangent point of the last segment.
(9) And (3) solving a matrix equation to obtain 4N unknowns of the matrix equation, wherein the 4N-3 to 4N unknowns are coefficients of the displacement deformation equation of the ith section of the drill string, so that the displacement deformation equations of the 1 st section to the Nth section of the drill string can be determined, and the rotation angle equation, the bending moment equation and the shear force equation of the 1 st section to the Nth section of the drill string can be obtained by derivation.
(10) Judging whether the bending moment value of the tail end of the last section of the push type rotary steering drilling tool assembly meets the requirement M-EIK, if yes, performing step 11, otherwise, reducing the range of the tangent length of the last section of the drilling tool assembly, and returning to step 8;
(11) obtaining equations of all units of the rotary steering drilling tool assembly and displacement curves, corner curves, bending moment curves and shear force curves of the rotary steering drilling tool assembly;
and (3) judging whether the bending moment value of the tail end of the last section of the push type rotary steering drilling tool combination meets the requirement M, namely EIK, and respectively sorting the displacement equation, the corner equation, the bending moment equation and the shear equation of the 1 st section to the Nth section of the drill string into piecewise functions according to the displacement equation, the corner equation, the bending moment equation and the shear equation, so that the displacement equation, the corner equation, the bending moment equation and the shear equation of the whole push type rotary steering drilling tool combination can be obtained. The displacement value of each point in the push-type rotary steering drilling tool combination is equal to the specific value of the displacement equation of the section, the turning angle value is equal to the first derivative of the turning angle equation of the section, the bending moment value is equal to the second derivative of the bending moment equation of the section and then multiplied by EI, and the shearing force value of each point is equal to the third derivative of the shearing force equation of the section and then multiplied by EI, so that a displacement function curve, a turning angle function curve, a bending moment function curve and a shearing force function curve of the whole push-type rotary steering drilling tool combination are obtained, and the displacement curve, the turning angle curve, the bending moment curve and the shearing force curve of the push-type rotary steering drilling tool combination can be obtained by drawing the function curves in MATLAB drawing software.
In the following, a specific embodiment of a bottom hole assembly in accordance with well parameters in vittawa, the displacement and deformation of which is analyzed as shown in fig. 4.
The first embodiment is as follows: the static pushing type rotary steering drilling tool combination structure and related parameters are as follows: phi 215.9mmPDC drill bit
+ phi 197mm rotary steering tool + phi 187mm drill collar + phi 212mm stabilizer + phi 135mm flexible pup joint + phi 171.45mm nonmagnetic drill collar.
The static push-against type rotary steerable drilling assembly comprises 5 variable stiffness (B, C, E, F, H), and the specific parameters are as follows:
TABLE 1 rotary steerable drilling tool assembly details
| Parameter(s) | Numerical value (Unit) |
| PDC bit diameter/length | 215.9(mm)/0.25(m) |
| Lower joint diameter/length | 171(mm)/0.2065(m) |
| Rotary steerable tool diameter/length | 197(mm)/1.63(m) |
| Center tube diameter/length | 187(mm)/1.24(m) |
| Drill collar diameter/length | 171.45(mm)/1.42(m) |
| Diameter of stabilizer | 212(mm) |
| Flexible nipple diameter/length | 135(mm)/1.03(m) |
| Diameter/length of non-magnetic drill collar | 171.45(mm)/7.776(m) |
| Weight on bit | 120(KN) |
| Density of drilling fluid | 1.13(kg/L) |
The first embodiment is analyzed by using the mechanical analysis method of the invention, and the steps are as follows (see the attached figure 6 in the specification):
(1) reasonably simplifying and equivalently processing the push-type rotary steering drilling tool assembly;
the deformation of the push-type rotary steering drilling tool combination comprising a drill bit, a rotary steering tool, a stabilizer, a flexible joint and a drill collar is assumed to be small elastic deformation; the diameter of the well hole is the diameter of the drill bit, and the well wall is a rigid body; the top end of the push-type rotary guide drilling tool assembly is tangent to the wall of the lower well under the influence of self weight, and the torsional deformation of the top end is not considered; due to the influence of the self weight of the drill string, the drill string above the tangent point of the tail end of the push-type rotary steering drilling tool assembly and the well wall is laid on the lower well wall; the contact form of the push-against type rotary steering drilling tool assembly and the well wall is a point contact form; the axis of the push-type rotary steering drilling tool assembly before deformation is the axis of the well bore, and an annular gap exists between the well walls; the stabilizer is simplified and processed into a drill rod with the center point contacting with the well wall and the rest being normal drill rods; the rib position is approximately regarded as a stabilizer with certain displacement; and defining the positions of a drill bit, a variable cross section, a stabilizer and a tangent point of the push-pull type rotary steering drilling tool assembly as the positions of nodes of the push-pull type rotary steering drilling tool assembly, and defining a section of drill string between the nodes.
(2) Carrying out stress analysis on the pushing type rotary steering drilling tool assembly micro element section to obtain a displacement deformation equation; taking a infinitesimal section with the length dx at any position of the push-pull type rotary steering drilling tool assembly, and carrying out stress analysis on the infinitesimal section, wherein P is an axial load and N; m is a section bending moment, N.m; q is a section shear force, N; q is uniformly distributed load, N/m; x is the length of the drill string, m; y is the displacement deformation of the drill string, m; e is the elastic modulus of the drill string material, Pa; i is the moment of inertia of the cross section, m4。
The force balance equation of the infinitesimal body is formula (1):
the equation of bending moment and curvature is formula (2):
the following formulas (1) and (2) are combined:
solving the displacement deformation equation of the infinitesimal section drill string by the equation (3) as follows:
order to
The deformation equation of displacement of the infinitesimal section drill string becomes:
in formula (5): unknown constant C1、C2、C3、C4The coefficient of the infinitesimal section drill string displacement deformation equation is obtained.
(3) Obtaining a corner equation, a bending moment equation and a shear force equation according to the displacement deformation equation;
the displacement deformation equation of any section (defined as the ith section of the push type rotary steering drilling tool assembly) of the drill string in the push type rotary steering drilling tool assembly calculates the first derivative, the second derivative and the third derivative of x:
yi″′＝ki 3Ci3sin(kixi)-ki 3Ci4cos(kixi)#(9)
the displacement of the drill string is y, the tangent angle is y ', the bending moment is M-EIy ', and the shearing force is F-EIy '.
The equation system composed of the formula (6), the formula (7), the formula (8) and the formula (9) has the form of matrix multiplication:
(4) obtaining a matrix equation of simultaneous displacement deformation equations of two adjacent sections of drill strings of the push type rotary steering drilling tool assembly according to the step (3);
any section of the push type rotary steering drilling tool assembly is defined as the ith section of the drill string of the push type rotary steering drilling tool assembly, the next section adjacent to the ith section is defined as the jth section of the push type rotary steering drilling tool assembly, and the displacement matrix equation of the ith section of the drill string and the jth section of the drill string are subtracted to obtain the matrix equation of the displacement deformation equation simultaneous of the adjacent sections of the drill string of the push type rotary steering drilling tool assembly as follows:
(5) determining a boundary condition and a continuity condition;
the connection mode of the node positions related to the push-type rotary steering drilling tool combination is divided into the following modes: a hinged connection mode, a variable cross-section connection mode, a stabilizer connection mode and a tangent connection mode. And respectively describing boundary conditions and continuity conditions of different connection modes.
a. Hinged connection (drill bit, only one section of drill string is related)
The drill bit of the push-type rotary steering drilling tool assembly is hinged, the displacement y is 0, the bending moment is EIy ″ -0, and the boundary conditions are as follows:
when formula (12) is taken into formula (11):
b. variable cross-section connection (drill string variable cross-section, relating two drill strings)
At the variable cross section between any two adjacent sections of drill columns of the push-type rotary steering drilling tool assembly, the displacement, the corner, the bending moment and the shearing force of the two sections of drill columns at the variable cross section are equal, and then the boundary conditions and the continuity conditions are as follows:
when formula (14) is taken into formula (11):
c. stabilizer connection mode (stabilizer between two drill columns contacting with well wall, associated two drill columns)
At the stabilizer of the push-type rotary steering drilling tool assembly, the displacement, the corner, the bending moment and the shearing force of the left and the right drill strings at the stabilizer are equal, and the displacement at the stabilizer is equal to half of the difference value between the diameter of the borehole and the outer diameter of the stabilizer, so that the boundary conditions and the continuity conditions are as follows:
when formula (16) is taken into formula (11):
d. tangent connection mode (tangent point and well wall tangent point, associated with a section of drill string)
The final section of the push-type rotary steering drilling tool assembly is at a tangent point tangent with the well wall, the rotating angle of the final section of the drill string at the tangent point is 0, the displacement is equal to half of the difference value between the diameter of the well and the outer diameter of the drill string, and the boundary condition and the continuity condition are as follows:
when formula (18) is introduced into formula (11):
formula (12) to formula (19): l isiThe length of the section i of the drill string of the push-pull type rotary steering drilling tool assembly is m; diThe outer diameter m of the ith section of a drill string of the push-pull rotary steering drilling tool assembly; d1Is the borehole diameter, m.
(6) Dividing the drilling tool assembly into units, inputting parameters and selecting a connection mode.
And dividing the push-pull type rotary steering drilling tool assembly into 8 sections of drilling strings according to the node positions, and setting the total number of the sections of the drilling strings divided by the push-pull type rotary steering drilling tool assembly to be 8. And (4) determining a connection mode according to the positions of the 9 nodes of the push-pull type rotary steering drilling tool assembly obtained in the step (5), and substituting the bit pressure parameters of the push-pull type rotary steering drilling tool assembly and the related parameters of 8 sections of drill strings (including the section length of the front 7 sections of drill strings and the outer diameter, the inner diameter, the elastic modulus and the uniform load of the 8 sections of drill strings) into the boundary condition and the continuity condition equation of the node positions in the step (5).
(7) The range of the length of the last drill string section of the push-against rotary steerable drilling assembly is given.
The end of the last section of the drill string of the push-against rotary steerable drilling assembly is in contact with the borehole wall, but at the tangent point of contact (i.e., the nth section of the drill string)Section length L of columnn) Is in practice uncertain. The bending moment value M according to the tangent point position is determined (M is 0 in the horizontal well and M is EIK in the inclined well (K is related to the well inclination angle)), so it is assumed that the drill string section length L can make the bending moment value M of the tangent point position of the nth drill string equal to EIKnBetween Lmin and Lmax. To find a drill string section length L that enables M to EIKnTo make the drill string section long LnStarting from Lmin and increasing to Lmax, finding L that can make M equal to EIKnThe value is obtained.
(8) For the push-pull type rotary steering drilling tool assembly divided into N sections, according to the boundary conditions and continuity condition equations of the N +1 node positions obtained in the steps (7) and (8), 4N equation sets containing 4N unknown numbers can be obtained by performing matrix splicing according to the node positions, and a linear matrix equation AX ═ B is formed through a mechanical model as follows:
wherein the matrix A is
Matrix B ═ 00.02580.00080.0065426151.0200.00030.0029-182258.1900.00790.00600.018100.00680.016886914.1100.01390.022477383.3400.01590.01390.0224110865.310.00360.0071-110865.3100.42410.1186'
(9) And (3) solving a matrix equation to obtain 24 unknowns of the matrix equation, wherein X is [ 5.97030.1378-5.9703-2.12181.26890.1313-1.2693-1.23993.32080.1284-3.3216-1.63513.4255-0.0543-3.42740.67122.4088-0.0711-2.41120.79901.4468-0.0935-1.4490.89620.06650.0722-0.0684-0.39481.3690.0651-1.3734-0.6582 ]', and the 4N-3 to 4N unknowns are coefficients of the displacement deformation equation of the ith section of the drill string, so that the displacement deformation equations of the 1 st section to the Nth section of the drill string can be determined, and the rotation angle equation, the bending moment equation and the shear force equation of the 1 st section to the Nth section of the drill string are obtained by solving the matrix equation AX which is obtained according to the step (8).
(10) Judging whether the bending moment value of the tail end of the last section of the push type rotary steering drilling tool assembly meets the requirement M-EIK, if yes, performing step 11, otherwise, reducing the range of the tangent length of the last section of the drilling tool assembly, and returning to step 8;
(11) obtaining equations of all units of the rotary steering drilling tool assembly and displacement curves, corner curves, bending moment curves and shear force curves of the rotary steering drilling tool assembly;
and (3) judging whether the bending moment value of the tail end of the last section of the push type rotary steering drilling tool combination meets the requirement M, namely EIK, and respectively sorting the displacement equation, the corner equation, the bending moment equation and the shear equation of the 1 st section to the Nth section of the drill string into piecewise functions according to the displacement equation, the corner equation, the bending moment equation and the shear equation, so that the displacement equation, the corner equation, the bending moment equation and the shear equation of the whole push type rotary steering drilling tool combination can be obtained. The displacement value of each point in the push-type rotary steering drilling tool combination is equal to the specific value of the displacement equation of the section, the turning angle value is equal to the first derivative of the turning angle equation of the section, the bending moment value is equal to the second derivative of the bending moment equation of the section and then multiplied by EI, and the shearing force value of each point is equal to the third derivative of the shearing force equation of the section and then multiplied by EI, so that a displacement function curve, a turning angle function curve, a bending moment function curve and a shearing force function curve of the whole push-type rotary steering drilling tool combination are obtained, and the displacement curve, the turning angle curve, the bending moment curve and the shearing force curve of the push-type rotary steering drilling tool combination can be obtained by drawing the function curves in MATLAB drawing software. The curves of the displacement deformation equation are shown in fig. 5.
The displacement value, the rotation angle value, the bending moment value and the shear force value of each node of the drilling tool assembly can be obtained through calculation, and are shown in table 2. Through analyzing data, it can be seen that displacement, corner, bending moment and shearing force at each point from A to F all meet boundary conditions and continuity conditions;
TABLE 2 Single-bend screw combination related checking data
The displacement data shows that the displacement of the A point of the drill bit is 0, the displacements of other points are continuous (the numerical values of the left side and the right side are equal), and the displacements of the D point, the G point and the tangent point K of the stabilizer are equal to half of the difference value between the borehole diameter and the outer diameter of the drill string, so that the boundary condition and the continuity condition of the displacements from the A point to the K point are met.
The corner data shows that the corners at all points are continuous (the values of the left side and the right side are equal), and the boundary condition and the continuity condition of the corners from A to K are met.
The bending moment data shows that the bending moment of the point A of the drill bit is 0, the bending moment of the point F of the tangent point is approximately 0, the bending moments of other points are continuous (the numerical values of the left side and the right side are equal), and the boundary condition and the continuity condition of the bending moments from the point A to the point K are met.
The shear force values of the points D and G of the stabilizer have a sudden change, the shear force values of other points are continuous (the values of the left side and the right side are equal), and the boundary condition and the continuity condition of the shear force from the point A to the point K are met.
According to the data obtained by calculation, the accuracy of the derivation formula and the model establishment is verified, so that the first example verifies the accuracy of the established mechanical model of the push type rotary steering drilling tool assembly.
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 analysis method of a push-pull type rotary steering drilling tool assembly is characterized by comprising the following steps: it comprises the following steps:
1) reasonably simplifying and equivalently processing the push-type rotary steering drilling tool assembly;
the deformation of the push-type rotary steering drilling tool combination comprising a drill bit, a rotary steering tool, a stabilizer, a flexible joint and a drill collar is assumed to be small elastic deformation; the diameter of the well hole is the diameter of the drill bit, and the well wall is a rigid body; the top end of the push-type rotary guide drilling tool assembly is tangent to the wall of the lower well under the influence of self weight, and the torsional deformation of the top end is not considered; due to the influence of the self weight of the drill string, the drill string above the tangent point of the tail end of the push-type rotary steering drilling tool assembly and the well wall is laid on the lower well wall; the contact form of the push-against type rotary steering drilling tool set and the well wall is a point contact form; the axis of the push-type rotary steering drilling tool assembly before deformation is the axis of the well bore, and an annular gap exists between the well walls; the stabilizer is simplified and processed into a drill rod with the center point contacting with the well wall and the rest being normal drill rods; the rib position is approximately regarded as a stabilizer with certain displacement; defining a drill bit, a variable cross section, a stabilizer and a tangent point of the push-pull type rotary steering drilling tool assembly as the node position of the push-pull type rotary steering drilling tool assembly, and defining a section of drill column between the nodes;
2) carrying out stress analysis on the pushing type rotary steering drilling tool assembly micro element section to obtain a displacement deformation equation; taking a infinitesimal section with the length dx at any position of the push-pull type rotary steering drilling tool assembly, and carrying out stress analysis on the infinitesimal section, wherein P is an axial load and N; m is a section bending moment, N.m; q is a section shear force, N; q is uniformly distributed load, N/m; x is the length of the drill string, m; y is the displacement deformation of the drill string, m; e is the elastic modulus of the drill string material, Pa; i is the moment of inertia of the cross section, m4；
The force balance equation of the infinitesimal body is formula (1):
the equation of bending moment and curvature is formula (2):
the following formulas (1) and (2) are combined:
solving the displacement deformation equation of the infinitesimal section drill string by the equation (3) as follows:
order to
The deformation equation of displacement of the infinitesimal section drill string becomes:
in formula (5): unknown constant C1、C2、C3、C4The coefficient of the infinitesimal section drill column displacement deformation equation is obtained;
3) obtaining a corner equation, a bending moment equation and a shear force equation according to the displacement deformation equation;
any section in the push type rotary steering drilling tool assembly is defined as a first derivative, a second derivative and a third derivative of x by a displacement deformation equation of an ith section of a drill string of the push type rotary steering drilling tool assembly:
yi″′＝ki 3Ci3sin(kixi)-ki 3Ci4cos(kixi)#(9)
the displacement of the drill string is y, the cutting angle is y ', the bending moment is M which is EIy ', and the shearing force is F which is EIy ';
the equation system composed of the formula (6), the formula (7), the formula (8) and the formula (9) has the form of matrix multiplication:
4) obtaining a matrix equation of simultaneous displacement deformation equations of two adjacent sections of drill strings of the push-type rotary steering drilling tool assembly according to the step 3);
any section of the push type rotary steering drilling tool assembly is defined as the ith section of the drill string of the push type rotary steering drilling tool assembly, the next section adjacent to the ith section is defined as the jth section of the push type rotary steering drilling tool assembly, and the displacement matrix equation of the ith section of the drill string and the jth section of the drill string are subtracted to obtain the matrix equation of the displacement deformation equation simultaneous of the adjacent sections of the drill string of the push type rotary steering drilling tool assembly as follows:
5) determining boundary conditions and continuity conditions;
the connection mode of the node positions related to the push-type rotary steering drilling tool combination is divided into the following modes: a hinged connection mode, a variable cross-section connection mode, a stabilizer connection mode and a tangent connection mode; respectively describing boundary conditions and continuity conditions of different connection modes;
a. a hinged connection mode;
the drill bit of the push-type rotary steering drilling tool assembly is hinged, the displacement y is 0, the bending moment is EIy ″ -0, and the boundary conditions are as follows:
when formula (12) is taken into formula (11):
b. a variable cross-section connection mode;
at the variable cross section between any two adjacent sections of drill columns of the push-type rotary steering drilling tool assembly, the displacement, the corner, the bending moment and the shearing force of the two sections of drill columns at the variable cross section are equal, and then the boundary conditions and the continuity conditions are as follows:
when formula (14) is taken into formula (11):
c. a stabilizer connection mode;
at the stabilizer of the push-type rotary steering drilling tool assembly, the displacement, the corner, the bending moment and the shearing force of the left and the right drill strings at the stabilizer are equal, and the displacement at the stabilizer is equal to half of the difference value between the diameter of the borehole and the outer diameter of the stabilizer, so that the boundary conditions and the continuity conditions are as follows:
when formula (16) is taken into formula (11):
d. a tangent connection mode;
the final section of the push-type rotary steering drilling tool assembly is at a tangent point tangent with the well wall, the rotating angle of the final section of the drill string at the tangent point is 0, the displacement is equal to half of the difference value between the diameter of the well and the outer diameter of the drill string, and the boundary condition and the continuity condition are as follows:
when formula (18) is introduced into formula (11):
formula (12) to formula (19): l isiThe length of the section i of the drill string of the push-pull type rotary steering drilling tool assembly is m; diThe outer diameter m of the ith section of a drill string of the push-pull rotary steering drilling tool assembly; d1Is the borehole diameter, m;
6) dividing the drilling tool assembly into units, inputting parameters and selecting a connection mode;
dividing the push-type rotary steering drilling tool assembly into a plurality of sections of drilling strings according to the node positions, and setting the total number of the sections of the drilling strings divided by the push-type rotary steering drilling tool assembly as N; determining a connection mode of the push-type rotary steering drilling tool assembly according to the N +1 node positions of the push-type rotary steering drilling tool assembly obtained in the step 5), and substituting the bit pressure parameters of the push-type rotary steering drilling tool assembly and the related parameters of N sections of drilling strings, including the section length of the N-1 sections of drilling strings and the outer diameter, the inner diameter, the elastic modulus and the uniformly distributed load of the N sections of drilling strings into the boundary condition and the continuity condition equation of the node positions in the step 5);
7) setting the section length range of the last section of the drill string of the push type rotary steering drilling tool assembly;
the tail end of the last section of the push type rotary steering drilling tool assembly is contacted with the well wall, but the tangent point position of the contact is the section length L of the Nth section of the drill stringnAnd is uncertain in practice; the bending moment value M according to the position of the tangent point is determined, M is 0 in the horizontal well, M is EIK in the inclined well, and the K value is related to the inclination angle; therefore it is assumed to enableThe bending moment value M of the tangent point position of the Nth section of the drill string is equal to the drill string section length L of EIKnBetween Lmin and Lmax; to find a drill string section length L that enables M to EIKnTo make the drill string section long LnStarting from Lmin and increasing to Lmax, finding L that can make M equal to EIKnA value;
8) and for the push-pull type rotary steering drilling tool assembly divided into N sections, carrying out matrix splicing according to the boundary conditions and continuity condition equations of the N +1 node positions obtained in the steps 6) and 7) and the node positions to obtain 4N equation sets containing 4N unknown numbers, and forming a linear matrix equation AX (B) through a mechanical model as follows:
in formula (20): a. the0Is a 2 x 4 matrix, which is a boundary condition coefficient matrix at the drill bit;
Ai＝(Ai1|Ai2) A 4 × 8 matrix (i ═ 1,2, …, N-1), which is a boundary condition coefficient matrix at the end of the ith segment; a. theNIs a 2 x 4 matrix which is a boundary condition coefficient matrix at the tail end tangent point of the last segment; xi＝[Ci1，Ci2，Ci3，Ci4]' is a 4 x 1 matrix, representing the unknown matrix of the i-th segment of the displacement function; b is0Is a 2 x 1 matrix, which is a matrix of boundary condition constants at the drill bit; b isiA 4 × 1 matrix (i ═ 1,2, …, N-1) is a boundary condition constant matrix at the end of the ith segment; b isNThe matrix is a 2 multiplied by 1 matrix and is a constant matrix of boundary conditions at the tangent point of the last section of the tail end;
9) performing matrix equation solution on the linear matrix equation AX ═ B obtained in the step 8) to obtain 4N unknowns of the matrix equation, wherein the 4N-3 to 4N unknowns are coefficients of the displacement deformation equation of the ith section of drill string, so that the displacement deformation equations of the 1 st section to the Nth section of drill string can be determined, and then derivation is performed on the displacement deformation equations to obtain a corner equation, a bending moment equation and a shear force equation of the 1 st section to the Nth section of drill string;
10) judging whether the bending moment value of the tail end of the last section of the push-type rotary steering drilling tool assembly meets the requirement M (EIK), if so, performing step 11), otherwise, reducing the range of the tangent length of the last section of the drilling tool assembly, and returning to step 8);
11) obtaining equations of all units of the rotary steering drilling tool assembly and displacement curves, corner curves, bending moment curves and shearing force curves of the rotary steering drilling tool assembly;
judging whether the bending moment value of the tail end of the last section of the push type rotary steering drilling tool combination obtained in the step 10) meets the requirement M-EIK, and respectively sorting the bending moment value of the last section of the push type rotary steering drilling tool combination into piecewise functions according to the displacement equation, the corner equation, the bending moment equation and the shear equation of the 1 st section to the Nth section of the drill string to obtain the displacement equation, the corner equation, the bending moment equation and the shear equation of the whole push type rotary steering drilling tool combination; the displacement value of each point in the push-type rotary steering drilling tool combination is equal to the specific value of the displacement equation of the section, the turning angle value is equal to the first derivative of the turning angle equation of the section, the bending moment value is equal to the second derivative of the bending moment equation of the section and then multiplied by EI, and the shearing force value of each point is equal to the third derivative of the shearing force equation of the section and then multiplied by EI, so that a displacement function curve, a turning angle function curve, a bending moment function curve and a shearing force function curve of the whole push-type rotary steering drilling tool combination are obtained, and the displacement curve, the turning angle curve, the bending moment curve and the shearing force curve of the push-type rotary steering drilling tool combination can be obtained by drawing the function curves in MATLAB drawing software.
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