A static push-the-bit rotary steerable drilling system dynamics analysis method

Abstract

The application provides a kind of static push type rotary steerable drilling system dynamics analysis method, comprising: according to the mechanical characteristics of static push type rotary steerable drilling system, the static push type rotary steerable drilling system is modularized; with the rigidly connected body structure in rotary steerable bottom hole assembly as the research object, the overall dynamics equation of the body structure is established; according to the tool structure and working characteristics of the static push type rotary steerable drilling system, the remaining modules except the body structure are treated as boundary conditions, and the corresponding boundary condition processing rule is proposed; based on the overall dynamics equation and the boundary condition processing rule, the rotary steerable bottom hole assembly dynamics model is constructed, and the dynamic characteristics at any position of the bottom hole assembly are solved. The application not only considers the real dynamic working condition of rotary steering, improves the calculation accuracy, but also makes targeted equivalent treatment, improves the calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of oil drilling tools and tubing mechanics, and more specifically, to a dynamic analysis method for a static push-type rotary steerable drilling system. Background Technology

[0002] Rotary steerable systems are a key technology for efficiently developing complex oil and gas reservoirs, representing the highest level of drilling technology today. Unlike traditional sliding steerable systems, rotary steerable systems can perform continuous, closed-loop trajectory control while the drill string is constantly rotating, greatly improving mechanical drilling speed and trajectory control accuracy.

[0003] Because rotary steerable systems are constantly rotating during operation, the drill string is constantly subjected to coupled vibrations in the lateral, longitudinal, and torsional directions, as well as complex loads such as tension, compression, bending, and torsion. Furthermore, dynamic interferences such as wellbore impact, drilling pressure, and torque exist, making the stress and vibration conditions of the tool downhole exceptionally complex. These high-precision measurement and control devices are highly sensitive to downhole vibrations, and system failures and inaccurate measurement data caused by vibration are common in the field. Therefore, understanding the mechanical characteristics of the drill string, especially the bottom drill string where the high-precision measurement and control device is located, is of great significance for predicting and controlling downhole vibrations in static push-type rotary steerable systems.

[0004] There are two difficulties in the existing research: (1) The drill string is a flexible body with a large slenderness ratio. It rotates at high speed in a narrow well filled with fluid and is subjected to coupled vibration, complex loads and random collisions. Due to the complexity of dynamic factors and nonlinear conditions, statics can no longer meet the research requirements. It is necessary to establish a drill string dynamics model that considers dynamic characteristics. (2) Due to the special tool structure and working principle of the static push-type rotary steering system, its guide head has mechanical structures such as drive shaft, non-rotating sleeve, and ribs. The drive shaft rotates at high speed with the drill string body structure. The non-rotating sleeve is connected to the drive shaft through two sliding bearings and thus basically remains stationary. The ribs are outside the non-rotating sleeve to support the well wall and provide the required guiding force to the drill bit. Its boundary conditions are relatively complex. It is necessary to study the tool structure in depth and give a targeted boundary condition treatment method.

[0005] Existing methods have failed to fully address the two problems mentioned above. To address these issues, this invention provides a dynamic analysis method for a static push-type rotary steerable drilling system. Summary of the Invention

[0006] To address the problems in the prior art, this invention provides a dynamic analysis method for a static push-type rotary steerable drilling system, the method comprising:

[0007] Based on the mechanical characteristics of the static push-type rotary steerable drilling system, the static push-type rotary steerable drilling system is modularized to construct multiple modules;

[0008] Taking the rigidly connected body structure in the rotary steerable bottom drill string as the research object, the overall dynamic equation of the body structure is established.

[0009] Based on the tool structure and working characteristics of the static push-type rotary steerable drilling system, all modules except the main body structure are treated as boundary conditions, and targeted boundary condition processing rules are proposed.

[0010] Based on the overall dynamic equation and the boundary condition processing rules, a dynamic model of the rotary steerable bottom drill string is constructed, and the dynamic characteristics at any position of the bottom drill string are solved.

[0011] According to one embodiment of the present invention, the module includes, but is not limited to: a top drive module, a drill pipe module, a bottom drill string module, a drill bit module, and a wellbore module, wherein the bottom drill string module includes various instruments and upper drill collars and weighted drill pipes in the static push-type rotary steerable drilling system, and the wellbore module is the wellbore trajectory formed by the drilling of the static push-type rotary steerable drilling system.

[0012] According to an embodiment of the present invention, the overall dynamic equation of the body structure is established through the following steps:

[0013] Three Cartesian coordinate systems were established: the wellhead coordinate system, the wellbore coordinate system, and the unit local coordinate system.

[0014] Based on the typical drill string structure of the static push-type rotary steerable drilling system, the main body structure is processed into a three-dimensional elastic beam with a variable cross section. The three-dimensional elastic beam is discretized at key locations using the finite element method and divided into Timoshenko beam elements with multiple nodes and degrees of freedom that can consider shear deformation.

[0015] The expressions for the kinetic energy, potential energy, and generalized force of the beam element are derived. Substituting these expressions into the Lagrange equations, the finite element dynamic equations of the beam element are derived. By combining the finite element dynamic equations corresponding to all beam elements, the overall dynamic equations of the body structure are obtained.

[0016] According to one embodiment of the present invention, the wellhead coordinate system is used to describe the wellbore trajectory with the wellhead position as the origin and due north, due east, and vertical depth as the coordinate axes. The wellbore coordinate system is used to describe the position and deformation of the bottom drill string with any node of the wellbore axis as the origin and the axis tangent, wellbore elevation, and torsional azimuth as the coordinate axes. The local coordinate system is used to describe the torsion of the bottom drill string axis with any node of the drill string axis as the origin and the drill string axis and drill string cross-section as the three coordinate axes.

[0017] According to one embodiment of the present invention, the key locations include, but are not limited to: the instrument end face, the variable cross-section location, and the location where the pushing force is applied.

[0018] According to one embodiment of the present invention, the three-dimensional elastic beam is discretized at the key location using the finite element method, and divided into multiple 2-node, 12-DOF Timoshenko beam elements that can consider shear deformation, wherein the nodal displacement vectors of the beam elements are expressed as:

[0019] {q e}=[u zi ,u xi ,u yi ,θ zi ,θ xi ,θ yi ,u zj ,u xj ,u yj ,θ zj ,θ xj ,θ yj ] T

[0020] Where, q e u is the nodal displacement vector of the beam element; z u x u y The displacements of the beam element nodes along the Z, X, and Y axes of the wellbore coordinate system are in meters (m); θ z θ x θ y denoted as rad, where z, x, y axes in the local coordinate system are the rotation angles of the beam element nodes relative to the Z, X, Y axes in the borehole coordinate system; i and j are the node numbers of the beam element.

[0021] According to one embodiment of the present invention, the overall dynamic equation of the body structure is expressed as:

[0022]

[0023] Where q is a generalized variable; [M] is the global mass matrix; [K] is the global stiffness matrix; [C] is the global damping matrix; and {F} is the global external force vector.

[0024] According to one embodiment of the present invention, the boundary condition processing rule includes the drill string-wellbore contact boundary, using the processing method of disk rotor and external constraint in rotor dynamics, adding a massless disk rotor at a preset contact point position, and using constant contact stiffness to describe the contact force between the drill string and the wellbore, specifically:

[0025]

[0026] Among them, F n χ is the contact force, N; χ is the gap between the drill string and the wellbore, m; K c is the contact stiffness, N / m, and is the equivalent stiffness coefficient between the drill string and the wellbore rock.

[0027] According to one embodiment of the present invention, the boundary condition processing rule includes a top drive boundary. The top drive hinges the upper end of the drill string at the center of the wellhead and drives the drill string to rotate clockwise at a fixed rotational speed. Therefore, the top drive boundary has three degrees of freedom constrained, with the circumferential direction constrained by a fixed clockwise rotational speed. Specifically:

[0028]

[0029] Among them, u z u x u y These represent the nodal displacements of the beam element in the wellbore coordinate system, in meters (m); θ z ω is the circumferential rotation angle of the beam element node, in rad; ω0 is the top drive speed, in r / min.

[0030] According to one embodiment of the present invention, the boundary condition processing rule includes a drill pipe equivalent boundary, which treats the drill pipe module as a torsion spring to connect the top drive and the bottom drill string, thereby transmitting rotational speed and torque. Specifically:

[0031]

[0032] Where, k t The equivalent torsional stiffness of the drill pipe is given in N·m; L p G is the drill pipe length, in meters; G is the shear modulus, in Pa; I is the shear modulus. z Let m be the polar moment of inertia of the beam element. 4 .

[0033] According to one embodiment of the present invention, the boundary condition processing rule includes the upper boundary of the bottom drill string, where the upper end of the bottom drill string is hinged at the center of the wellbore, i.e., constraining three degrees of freedom of displacement, specifically:

[0034] u z (0)=u x (0)=u y (0)=0

[0035] Among them, u z u x u y These are the nodal displacements of the beam element in the wellbore coordinate system, in meters.

[0036] According to one embodiment of the present invention, the boundary condition processing rule includes the drill bit equivalent boundary. The lower end of the bottom drill string contacts the formation through the drill bit and is subject to drilling pressure and torque from wellbore constraints and the reverse action of the formation. The drill bit is considered as a full-width boundary, meaning that the two lateral displacement degrees of freedom of the drill bit node are constrained, specifically:

[0037] u x (L b )=u y (L b ) = 0

[0038] Among them, u x u y These represent the nodal displacements of the beam element in the wellbore coordinate system, in meters (m); L b The length of the bottom drill string is in meters (m).

[0039] During rock breaking, the drilling pressure fluctuates with the torsion of the drill bit. The drilling pressure can be treated as a sinusoidal function that varies with the drill bit rotation angle, specifically:

[0040] W b =W0+ζW0sin(nθ) zb )

[0041] Among them, W b denoted as N, where N is the actual drilling pressure at the drill bit; W0 is the steady-state amplitude of the drilling pressure, N; ζ is the drilling pressure fluctuation amplitude, which is related to the longitudinal vibration of the drill bit; n is the excitation factor; θ zb The drill bit rotation angle is expressed in rad.

[0042] The magnitude of the drill bit counter-torque can be categorized into three cases based on the drill bit's motion state and the active torque applied by the drill string: viscous phase, viscous-to-slip transition, and slip phase, specifically:

[0043]

[0044] Among them, T b The actual torque at the drill bit is N·m; G is the shear modulus, Pa; I z Let m be the polar moment of inertia of the beam element. 4 ;l e θ is the length of the lowest beam element, in meters; z1 θ is the circumferential rotation angle of the drill bit node, in rad; z2 Let ω be the circumferential rotation angle of a node on the drill bit, expressed in rad. bδ is the drill bit rotation speed, r / min; δ is the critical rotation speed of the viscous phase, r / min; b Drill bit outer diameter, m; μ s μ is the static friction coefficient. k d is the coefficient of kinetic friction; c γ is the attenuation coefficient; eq It represents the slip ratio.

[0045] According to one embodiment of the present invention, the boundary condition processing rule includes an equivalent boundary for a non-rotating outer sleeve. The non-rotating outer sleeve is supported on the drive shaft by upper and lower sliding bearings and is non-rigidly connected to the drive shaft. It is a non-rotating structure independent of the rotary guide bottom drill bit. The non-rotating outer sleeve is processed as an equivalent mass block attached to the drive shaft where the upper and lower sliding bearings are located, specifically as follows:

[0046]

[0047] Where, m n The mass of the non-rotating sliding sleeve is expressed in kg and m. u The equivalent mass of the upper sliding bearing is kg; A u Let m be the cross-sectional area of ​​the upper sliding bearing. 2 ;l u The length of the upper sliding bearing is in meters (m). d The equivalent mass of the lower sliding bearing is kg; A d Let m be the cross-sectional area of ​​the lower sliding bearing. 2 ;l d ρ is the length of the lower sliding bearing, in meters; ρ is the density of the guide head steel, in kilograms per cubic meter of water. 3 .

[0048] According to one embodiment of the present invention, the boundary condition processing rule includes a rib pushing force boundary. The rib pushing force refers to the lateral cutting force applied to the drill bit by pushing against the well wall through retractable ribs during drilling, thereby achieving real-time guidance during rotary drilling. The guiding force can be equivalent to two concentrated forces of constant magnitude and direction acting on the upper and lower sliding bearings, specifically:

[0049]

[0050] Among them, F steer For the rib thrust, N; f u The guiding force at the upper sliding bearing is N; f d The guiding force at the lower sliding bearing is N; n The length of the non-rotating outer jacket is in meters (m); l s1 The distance from the point of action of the rib to the upper sliding bearing is in meters (m); l s2 The distance from the point of action of the rib to the lower sliding bearing is in meters (m); l u The length of the upper sliding bearing is in meters (m); ld The length of the lower sliding bearing is in meters (m).

[0051] When the guiding force acts on the upper and lower sliding bearings, it will generate an additional torque, specifically:

[0052]

[0053] Among them, M u The torque at the upper sliding bearing is N·m; r u M is the radius of the male axis of the upper sliding bearing, in meters. d The torque at the lower sliding bearing is N·m; r d Let be the radius of the male axis of the lower sliding bearing, in meters (m).

[0054] According to one embodiment of the present invention, the boundary condition processing rule includes initial deformation processing of the drill string in a curved wellbore. Due to the constraint of the curved wellbore, the rotary guide bottom drill string will undergo initial deformation, that is, the drill string changes from a straight state to a curved state coinciding with the wellbore axis. For the bottom drill string discrete as beam elements, the initial deformation of the bottom drill string under the constraint of the curved wellbore can be represented by applying an initial displacement at the beam element node, that is, the straight drill string can be processed into a shape coinciding with the wellbore axis. The initial displacement at any beam element node is specifically as follows:

[0055]

[0056] Where N is the north-south coordinate of the well trajectory, in meters; E is the east-west coordinate of the well trajectory, in meters; D is the vertical depth of the well trajectory, in meters; s is the well depth of the well trajectory, in meters; and α is the inclination angle, in degrees. θ is the azimuth angle, °; i is the node number of the beam element; l e , where is the length of the lowest beam element, in meters.

[0057] According to one embodiment of the present invention, the dynamic model of the rotary steerable bottom drill string is solved using the second-order accuracy HHT-α implicit method. At any time, the overall dynamic equation of the main body structure is rewritten according to the HHT-α recursive formula as follows:

[0058]

[0059] Where [M] is the global mass matrix; [K] is the global stiffness matrix; [C] is the global damping matrix; {F} is the global external force vector; t is time, s; Δt is the minimum time interval, s; {q t+Δt} represents the displacement at time t + Δt; The velocity at time t+Δt; Let q be the acceleration at time t+Δt; t} represents the displacement at time t; Let α be the velocity at time t;h These are the damping control parameters.

[0060] According to one embodiment of the present invention, the dynamic characteristics include, but are not limited to, dynamic load spectrum, stress spectrum, strain spectrum, displacement spectrum, and acceleration spectrum.

[0061] According to another aspect of the invention, a storage medium is also provided, which includes a series of instructions for performing the steps of the method as described in any of the preceding claims.

[0062] This invention provides a dynamic analysis method for a static push-type rotary steerable drilling system. It considers the actual dynamic working conditions of the rotary steerable, improving calculation accuracy, and also performs targeted equivalent processing, improving calculation efficiency. This invention provides a bottom drill string dynamics modeling method and boundary condition processing method that considers the actual working state and structural characteristics of the static push-type rotary steerable. It employs a second-order accuracy HHT-α implicit method for solution, enabling accurate, efficient, and low-cost pre-drilling prediction and post-drilling analysis of the bottom drill string safety of the rotary steerable. This lays the theoretical foundation for the development of a data-driven virtual simulation system for the dynamic characteristics of static push-type rotary steerables.

[0063] Other features and advantages of the invention will be set forth in the description which follows, and some of these will be obvious from the description or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the description, claims and drawings. Attached Figure Description

[0064] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with the embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0065] Figure 1 A flowchart of a dynamic analysis method for a static push-type rotary steerable drilling system according to an embodiment of the present invention is shown;

[0066] Figure 2 Three coordinate systems are shown according to an embodiment of the present invention;

[0067] Figure 3 A schematic diagram of a typical drill string structure for a static push-type rotary steerable drilling system according to an embodiment of the present invention is shown;

[0068] Figure 4 A schematic diagram of a three-dimensional elastic beam of a bottom drill body structure according to an embodiment of the present invention is shown;

[0069] Figure 5A schematic diagram of a 2-node, 12-DOF Timoshenko beam element according to an embodiment of the present invention is shown;

[0070] Figure 6 A schematic diagram of the centrifugal force of a drill string rotation according to an embodiment of the present invention is shown;

[0071] Figure 7 A micro-element model of a wellbore trajectory according to an embodiment of the present invention is shown;

[0072] Figure 8 The dynamic transverse acceleration spectrum of reverse vortex at a flexible short section according to an embodiment of the present invention is shown.

[0073] Figure 9 The dynamic lateral acceleration spectrum during stick-slip at a flexible short section according to an embodiment of the present invention is shown;

[0074] Figure 10 The dynamic longitudinal acceleration spectrum during drill bit skipping at a drill bit location according to an embodiment of the present invention is shown;

[0075] Figure 11 A schematic diagram of the dynamic lateral force of a drill bit according to an embodiment of the present invention is shown.

[0076] In the accompanying drawings, the same parts use the same reference numerals. Also, the drawings are not drawn to scale. Detailed Implementation

[0077] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0078] Because different types of rotary steering systems operate on significantly different principles, different mechanical modeling methods and boundary condition handling methods are required for corresponding mechanical analyses. Currently, mature domestically developed rotary steering systems in my country are all static push-type, but there is no specific method for bottom drill string dynamic analysis. Only a few related patents or papers have been published, but all of them have certain shortcomings. Some studies only focus on static analysis of push-type or pointing-type rotary steering systems, lacking dynamic research that more closely reflects the actual rotary drilling state (e.g., CN111428385B and CN111428384B); some studies focus on dynamic theoretical modeling of conventional tools, without addressing the special structure and corresponding boundary conditions of the rotary steering system (e.g., CN113065211B); some studies conduct multibody dynamics software simulation research on rotary steering systems, but lack targeted boundary condition handling methods, and their multibody dynamics software simulation research methods do not involve theoretical modeling based on beam-column theory and finite element methods (e.g., CN102063541B); some studies, although focusing on static push-type rotary steering systems, still lack targeted boundary condition handling methods, failing to realistically consider boundary conditions such as the non-rotating outer jacket, rib pushing force, drill bit dynamic drilling pressure, and counter-torque of the static push-type rotary steering system, and the solution methods need further optimization (study on the mechanical properties and drilling trend of static push-type rotary steering BHA).

[0079] Figure 1 A flowchart of a dynamic analysis method for a static push-type rotary steerable drilling system according to an embodiment of the present invention is shown.

[0080] like Figure 1 As shown, in step S1, the static push-type rotary steerable drilling system is modularized according to its mechanical characteristics to construct multiple modules.

[0081] In one embodiment, the module includes, but is not limited to: a top drive module, a drill pipe module, a bottom drill string module, a drill bit module, and a wellbore module. The top drive module provides power to the entire drill string system. The drill pipe module connects the top drive to the bottom drill string and transmits the top drive force to the bottom drill string. The bottom drill string module includes various instruments in the rotary steerable system, as well as the upper drill collar and weighted drill pipe. The drill bit module is a PDC drill bit for the rotary steerable system used for rock breaking. The wellbore module represents the wellbore trajectory formed by the static push-type rotary steerable drilling system, which can be classified into straight wellbores and curved wellbores based on their geometry.

[0082] In this invention, the static push-type rotary steerable drilling system is modularized according to the different functions and characteristics of various components. This facilitates targeted boundary condition equivalence processing during modeling and results extraction during post-processing. For the dynamic analysis of static push-type rotary steerable drilling systems, existing technologies do not currently employ a modular processing approach similar to that of this invention.

[0083] like Figure 1 As shown, in step S2, the rigidly connected body structure of the rotary steerable bottom drill string is taken as the research object, and the overall dynamic equation of the body structure is established. Specifically, the rigidly connected body structure of the rotary steerable bottom drill string is taken as the main research object, and the three-dimensional beam element finite element dynamic equation corresponding to the body structure of the rotary steerable bottom drill string is established based on the Lagrange equation.

[0084] In one embodiment, in step S2, three Cartesian coordinate systems are established: the wellhead coordinate system O-NED, the wellbore coordinate system o-XYZ, and the element local coordinate system o'-xyz. Figure 2 As shown. Specifically, the wellhead coordinate system O-NED takes the wellhead position O as its origin and uses north (N-axis), east (E-axis), and vertical depth (D-axis) as its coordinate axes to describe and calculate the wellbore trajectory. The wellbore coordinate system o-XYZ takes any node on the wellbore axis as its origin o and uses the axis tangent (upper tangent direction as the Z-axis), the wellbore elevation (Y-axis), and the torsional azimuth direction (X-axis determined by the right-hand rule) as its coordinate axes to describe the position and deformation of the bottom drill string. The local coordinate system o'-xyz takes any node on the drill string axis as its origin o' and uses the drill string axis and drill string cross-section as its three coordinate axes to describe the torsion of the bottom drill string axis. Further, the local coordinate system o'-xyz takes any node on the drill string axis o' as its origin, with the z-axis pointing above the unit axis, the y-axis and x-axis located within the drill string cross-section and perpendicular to each other. When the drill string is not deformed, the y-axis coincides with the Y-axis, and the x-axis is determined according to the right-hand rule. The local coordinate system o'-xyz is mainly used to describe the torsion of the bottom drill string axis, which changes position and orientation continuously as the beam element deforms and rotates.

[0085] In one embodiment, in step S2, based on the typical drill string structure of a static push-type rotary steerable drilling system, the main body structure is processed into a three-dimensional elastic beam with a variable cross-section. The three-dimensional elastic beam is then discretized at key locations using the finite element method, dividing it into Timoshenko beam elements with multiple nodes and degrees of freedom that can account for shear deformation. In one embodiment, key locations include, but are not limited to: the instrument end face, the variable cross-section location, and the location where the push-type force is applied.

[0086] Specifically, based on the typical drill string structure of a static push-type rotary steerable drilling system (see...), Figure 3The rigidly connected body structure in the bottom drill module is treated as a three-dimensional elastic beam with a variable cross-section (see...). Figure 4 The beam is assumed to have uniform geometry and material properties, and its deformation is always within the linear elastic range. Using the finite element method, the entire three-dimensional elastic beam is discretized at key locations such as the instrument end face, the variable cross-section location, and the point of application of the pushing force, and divided into multiple 2-node, 12-DOF Timoshenko beam elements that can consider shear deformation (see...). Figure 5 ), where the nodal displacement vector of the beam element is expressed as:

[0087] {q e}=[u zi ,u xi ,u yi ,θ zi ,θ xi ,θ yi ,u zj ,u xj ,u yj ,θ zj ,θ xj ,θ yj ] T (1)

[0088] Where, q e u is the nodal displacement vector of the beam element; z u x u y The displacements of the beam element nodes along the Z, X, and Y axes of the wellbore coordinate system are in meters (m); θ z θ x θ y denoted as rad, where z, x, y axes in the local coordinate system are the rotation angles of the beam element nodes relative to the Z, X, Y axes in the borehole coordinate system; i and j are the node numbers of the beam element.

[0089] In one embodiment, in step S2, the expressions for the kinetic energy, potential energy, and generalized force of the beam element are derived. These expressions are then substituted into the Lagrange equations to derive the finite element dynamic equations for the beam element. Finally, the finite element dynamic equations corresponding to all beam elements are combined to obtain the overall dynamic equations of the body structure. Specifically, based on Timoshenko beam theory, the expressions for the kinetic energy, potential energy, and generalized force of the beam element are derived. Kinetic energy is divided into translational kinetic energy and rotational kinetic energy, and potential energy refers to elastic potential energy. Gravity is considered a conservative force, and generalized forces are divided into conservative and non-conservative forces. The expressions for kinetic energy, potential energy, and generalized force are substituted into the Lagrange equations to derive the finite element dynamic equations for the beam element. Finally, the dynamic equations of all beam elements are combined to establish the overall dynamic equations of the rotary guide bottom drill body structure.

[0090] The fundamental theory behind the dynamic equations of a rotary steerable bottom drill string is the Lagrange equation, which needs to be expressed using the kinetic energy, potential energy, and generalized forces of beam elements. The Lagrange equation can be expressed as:

[0091]

[0092] Among them, T e Let J be the kinetic energy of the beam element; U be the kinetic energy. e Let J be the potential energy of the beam element; q be the potential energy. e F is the nodal displacement vector of the beam element; e Let N be the generalized force of the beam element. The points on the generalized variable represent the derivative of that variable with respect to time.

[0093] When calculating the translational kinetic energy, assuming that the center of mass and the centroid of the drill string section coincide, it can be represented by the translational displacement of the element's axis. Therefore, the translational kinetic energy T of the beam element... t It can be represented as:

[0094]

[0095] Where ρ is the density of the drill string, kg / m³ 3 A is the cross-sectional area, m 2 ;u z u x u y The displacements of the beam element nodes along the Z, X, and Y axes of the wellbore coordinate system are in meters (m); l e Let be the length of the beam element, in meters (m).

[0096] The rotational velocity of the beam element can be represented by the Euler angles (η,ψ,γ) between the local coordinate system and the borehole coordinate system, and its expression in the borehole coordinate system is as follows:

[0097]

[0098] Among them, e z e x e y These are the unit vectors for the Z, X, and Y axes of the wellbore coordinate system, respectively.

[0099] Since the wellbore restricts the lateral movement of the drill string, the rotation angle of the drill string cross-section can be considered small. Therefore, the rotation angles of the beam element cross-section around the z, x, and y axes are considered to be approximately equal to the rotation angles around the Z, X, and Y axes. Hence: γ≈θ z η≈θ x ψ≈θ y Then the rotational kinetic energy T of the beam element r It can be represented as:

[0100]

[0101] Where ρ is the density of the drill string, kg / m³ 3 ;l e θ is the length of the beam element, in meters; z θ x θ y Let I be the nodal rotation angle of the beam element relative to the Z, X, Y axes of the borehole coordinate system in the local coordinate system, expressed in rad. z Let m be the polar moment of inertia of the beam element. 4 ;I xy Let m be the moment of inertia of the cross section of the beam element. 4 .

[0102] If the translational and rotational kinetic energies of the beam element are superimposed, then the total kinetic energy T of the beam element is... e It can be represented as:

[0103]

[0104] When deriving the dynamic equations of the drill string, the potential energy of the beam element generally refers to the elastic potential energy, and gravity is considered a conservative force. The elastic potential energy can be calculated based on the stress and strain of the drill string after deformation under stress. Both stress and strain have six terms, which can be expressed as follows:

[0105] σ=[σ zz ,σ xx ,σ yy ,τ zx ,τ zy ,τ xy ] T (7)

[0106] ε=[ε zz ,ε xx ,ε yy ,γ zx ,γ zy ,γ xy ] T (8)

[0107] Where σ is the stress vector, Pa; σ zz σ xx σ yy τ zx τ zy τ xy There are 6 stresses, Pa; ε is the strain vector; ε zz ε xx ε yy γ zx γ zy γ xy There are 6 strains.

[0108] Since the drill string material is linearly elastic, the stress-strain relationship of the drill string is governed by the generalized Hooke's law, and its elastic matrix can be expressed as:

[0109]

[0110] Where E is the elastic modulus (Pa); G is the shear modulus (Pa); v is Poisson's ratio; and λ is a function of Poisson's ratio, which can be expressed as:

[0111]

[0112] The potential energy of a beam element can be expressed by stress and strain as follows:

[0113]

[0114] For a drill string, which has a large slenderness ratio, the stress that contributes to the strain energy is considered to be the stress on the cross-section, therefore σ is considered to be... xx =σ yy =τ xy =0. According to the generalized Hooke's law, γ = 0. xy =0, ε xx =ε yy =-vε zz Then the potential energy of the beam element can be expressed as:

[0115]

[0116] Before calculating the potential energy of the beam element, we first calculate the strain. Since the drill string has a large slenderness ratio, we assume that the strain is only related to deformation and is not affected by rotation. Using Green's strain formula, which is unaffected by rotation, the strain can be expressed as:

[0117]

[0118] Where c1, c2, and c3 are the three directions of the coordinate axes.

[0119] The strain in the three directions in formula (12) can be expressed as follows:

[0120]

[0121] Assuming that the three translational displacement variables of the drill string under load and bending torque are independent, the displacement of any point on the beam element section can be expressed as:

[0122]

[0123] Among them, u z0 u x0 u y0Let m be the initial position of the beam element in the local coordinate system; x and y are the coordinates of any point on the cross section in the local coordinate system.

[0124] In the above formula, the displacement variable u z u x u y and rotation angle variable θ z θ x θ y Both are functions of the z-coordinate in the local coordinate system. Furthermore, according to beam theory, the relationship between deflection and rotation angle can be obtained:

[0125]

[0126] Substituting equations (14) to (16) into equation (12) and ignoring higher-order minor quantities, we can obtain the potential energy of a single beam element:

[0127]

[0128] Since the drill string is not perfectly axisymmetric in engineering, and its center of mass and centroid do not coincide, centrifugal force will inevitably be generated when the drill string rotates. When the drill string contacts the wellbore, contact force is generated due to the constraint of the wellbore, which will change the nodal forces and nodal displacements of the drill string, and simultaneously generate frictional force and frictional torque. This will be derived in detail in the boundary conditions. Gravity, centrifugal force, and contact force are considered conservative forces, while frictional force and frictional torque are considered non-conservative forces. In the overall dynamic equations, the viscous force of the fluid and the internal friction of the material are considered as linear Rayleigh damping. Specifically, the components of the beam element along the x, y, and z axes can be expressed as follows:

[0129]

[0130] Where, q l q represents the buoyancy of the drill string, in N / m. lx q ly q lz The buoyancy of the drill string is expressed in N / m along the x, y, and z axes.

[0131] The centrifugal force of the drill string can be divided into revolution centrifugal force and rotation centrifugal force. The revolution centrifugal force is already included in the kinetic energy term. The rotation centrifugal force of the drill string is taken as the external force vector (e.g., Figure 6 (As shown). The centrifugal force of rotation can be decomposed along the x-axis and y-axis of the local coordinate system as follows:

[0132]

[0133] Among them, f rx f is the centrifugal force per unit length of the drill string along the x-axis, in N; ryω is the centrifugal force per unit length of the drill string along the y-axis, in N; ω is the rotational speed, in r / min; β is the angle between the line connecting the centroid and the center of mass and the x-axis, in rad.

[0134] Substituting the expressions for the kinetic energy, potential energy, and generalized force of the beam element into the Lagrange equations, we can obtain the dynamic equations for a single beam element. Specifically:

[0135]

[0136] Among them, [M e [K] represents the mass matrix of the beam element; e ] is the stiffness matrix of the beam element; {F e} represents the external force vector of the beam element; [C e ] represents the damping matrix of the beam element.

[0137] For drilling engineering problems, it is difficult to directly calculate the viscous damping of the drill string caused by drilling fluid and the structural damping caused by internal friction of the material. Therefore, Rayleigh damping is used to represent it. Specifically:

[0138] [C e ]=α v [M e ]+β s [K e ] (twenty one)

[0139] Where, α v β is the viscous damping coefficient; s The structural damping coefficient. Viscous damping coefficient α. v A viscous damping proportional to the mass matrix is ​​defined, representing the damping caused by external factors of the material, i.e., the energy loss due to the viscosity of the drilling fluid; the structural damping coefficient β s Structural damping proportional to the stiffness matrix is ​​defined, representing the damping within the material, i.e., the energy loss caused by internal friction within the material.

[0140] The aforementioned kinetic energy matrix, potential energy matrix, damping matrix, and generalized force vector are all derived for a single beam element in the wellbore coordinate system. To form the overall dynamic equations, the parameters are first transformed into the wellhead coordinate system, because the inclination and azimuth angles of each beam element in a curved wellbore are different. Then, the dynamic equations of the individual beam elements are combined. Specifically:

[0141]

[0142] Where [O] is the beam element matrix expression in the wellhead coordinate system; [o] is the beam element matrix expression in the wellbore coordinate system; [H] is the direction cosine matrix between the wellhead coordinate system and the wellbore coordinate system, which can be expressed as:

[0143]

[0144] Where α is the well inclination angle, in °; The azimuth angle is in degrees.

[0145] By combining the dynamic equations of all beam elements, the overall dynamic equation of the rotary steerable bottom drill string structure can be formed, which can be expressed as:

[0146]

[0147] Where q is a generalized variable; [M] is the global mass matrix; [K] is the global stiffness matrix; [C] is the global damping matrix, which uses the Ruili damping matrix to represent the energy loss caused by the viscous damping of the drill string by the drilling fluid and the structural damping of the drill string material itself; and {F} is the global external force vector.

[0148] This invention optimizes the drill string dynamics equations: By comprehensively considering various influencing factors and focusing on key research objects to improve computational efficiency, this invention takes the rigidly connected body structure of the static push-type rotary steerable bottom drill string as the main research object. All modules except the body structure are treated as boundary conditions, unlike existing technologies that only consider the non-rigidly connected external structure of the bottom drill string and ignore the influence of the important upper drill pipe module. This invention considers the shear effect of beams, treating the body structure as a Timoshenko beam for dynamics equation derivation, instead of the Euler beam used in existing technologies, resulting in more reasonable calculation results.

[0149] like Figure 1 As shown, in step S3, based on the tool structure and working characteristics of the static push-type rotary steerable drilling system, all modules except the main body structure are treated as boundary conditions, and targeted boundary condition processing rules are proposed. Specifically, based on the special tool structure and working characteristics of the static push-type rotary steerable drilling system, all modules except the bottom drill string body structure are treated as boundary conditions, and eight targeted boundary condition processing rules are proposed. Further, the boundary condition processing rules include, but are not limited to: drill string-wellbore contact boundary, top drive boundary, drill pipe equivalent boundary, bottom drill string upper boundary, drill bit equivalent boundary, non-rotating outer sleeve equivalent boundary, rib push-force boundary, and initial deformation treatment of the drill string in a curved wellbore.

[0150] In one embodiment, the drill string-wellbore contact boundary is assumed to be a continuous, uniform, rigid cylinder with a continuous inner wall. The contact is considered discontinuous, and a method from rotor dynamics for handling disk rotors and external constraints is used. A massless disk rotor with an outer diameter equal to the drill string's outer diameter is added at a predetermined contact point. The intermediate process of elastic deformation and recovery of the wellbore is ignored during contact; the contact is treated as an instantaneous process, and a constant contact stiffness is used to describe the contact force between the drill string and the wellbore. Specifically:

[0151]

[0152] Among them, F n χ is the contact force, N; χ is the gap between the drill string and the wellbore, m; K c is the contact stiffness, N / m, and is the equivalent stiffness coefficient between the drill string and the wellbore rock.

[0153] Since the coefficient of friction includes both dynamic and static friction, the conversion relationship between dynamic and static friction in the contact model is represented by the exponentially decaying friction model:

[0154]

[0155] Where, μ k μ is the coefficient of kinetic friction. s d is the static friction coefficient; c γ is the attenuation coefficient; eq It represents the slip ratio.

[0156] Tangential friction can be expressed as:

[0157] F τ =μF n (27)

[0158] Among them, F τ The force is tangential friction, N.

[0159] Decomposing the radial contact force and tangential friction force along the X and Y axes, we can express them as follows:

[0160]

[0161] Among them, F x Force acting along the X-axis, N; F y The force acting along the Y-axis is in N.

[0162] When the drill string contacts the wellbore, an additional frictional torque is generated, which can be expressed as:

[0163] M τ =rF τ (29)

[0164] Among them, M τThe frictional torque caused by contact is expressed in N·m.

[0165] In one embodiment, the top drive boundary is defined as follows: the top drive hinges the upper end of the drill string at the center of the wellhead and rotates the drill string clockwise at a fixed rotational speed. In this case, the top drive boundary has three degrees of freedom constrained, with the circumferential direction constrained by a fixed clockwise rotational speed. Specifically:

[0166]

[0167] Among them, u z u x u y These represent the nodal displacements of the beam element in the wellbore coordinate system, in meters (m); θ z ω is the circumferential rotation angle of the beam element node, in rad; ω0 is the top drive speed, in r / min.

[0168] In one embodiment, the drill pipe equivalent boundary, during rotary drilling, shows that the bottom drill string module significantly affects the dynamic characteristics of the rotary steering system, while the upper drill pipe module has a smaller impact. To improve computational efficiency, the drill pipe module is equivalent to a torsion spring connecting the top drive and the bottom drill string, serving to transmit rotational speed and torque, specifically as follows:

[0169]

[0170] Where, k t The equivalent torsional stiffness of the drill pipe is given in N·m; L p G is the drill pipe length, in meters; G is the shear modulus, in Pa; I is the shear modulus. z Let m be the polar moment of inertia of the beam element. 4 .

[0171] In one embodiment, the upper boundary of the bottom drill string is treated similarly to the top drive boundary, since the upper drill pipe module is equivalent to a torsion spring connecting the top drive and the bottom drill string. That is, the upper end of the bottom drill string is hinged at the center of the wellbore, thus constraining three degrees of freedom of displacement. Specifically:

[0172] u z (0)=u x (0)=u y (0)=0 (32)

[0173] Among them, u z u x u y These are the nodal displacements of the beam element in the wellbore coordinate system, in meters.

[0174] In one embodiment, the drill bit equivalent boundary, with the lower end of the bottom drill string contacting the formation through the drill bit, is subject to wellbore constraints and the reverse drilling pressure and torque from the formation. The drill bit is considered a full-width boundary, meaning that the two lateral displacement degrees of freedom of the drill bit node are constrained, specifically:

[0175] u x (L b )=u y (L b )=0 (33)

[0176] Among them, u x u y These represent the nodal displacements of the beam element in the wellbore coordinate system, in meters (m); L b , where is the length of the bottom drill string, in meters (m).

[0177] During rock breaking, the drilling pressure fluctuates with the torsion of the drill bit. Therefore, the drilling pressure is treated as a function that varies sinusoidally with the drill bit rotation angle, specifically:

[0178] W b =W0+ζW0sin(nθ) zb (34)

[0179] Among them, W b denoted as N, where N is the actual drilling pressure at the drill bit; W0 is the steady-state amplitude of the drilling pressure, N; ζ is the drilling pressure fluctuation amplitude, which is related to the longitudinal vibration of the drill bit; n is the excitation factor; θ zb The drill bit rotation angle is expressed in rad.

[0180] The magnitude of the drill bit counter-torque can be categorized into three cases based on the drill bit's motion state and the active torque applied by the drill string: viscous phase, viscous-to-slip transition, and slip phase, specifically:

[0181]

[0182] Among them, T b The actual torque at the drill bit is N·m; G is the shear modulus, Pa; I z Let m be the polar moment of inertia of the beam element. 4 ;l e θ is the length of the lowest beam element, in meters; z1 θ is the circumferential rotation angle of the drill bit node, in rad; z2 Let ω be the circumferential rotation angle of a node on the drill bit, expressed in rad. b δ is the drill bit rotation speed, r / min; δ is the critical rotation speed of the viscous phase, r / min; b D is the outer diameter of the drill bit, in meters (m); d c γ is the attenuation coefficient; eq It represents the slip ratio.

[0183] In one embodiment, the equivalent boundary of the non-rotating outer sleeve is a unique feature of the static push-type rotary steer compared to other rotary steers. The guide head of the static push-type rotary steer contains mechanical structures such as a drive shaft, a non-rotating outer sleeve, and ribs. The drive shaft rotates at high speed continuously along with the drill string body. The non-rotating outer sleeve is supported on the drive shaft by upper and lower sliding bearings, and is non-rigidly connected to the drive shaft. It is a non-rotating structure independent of the bottom drill string of the rotary steer. The non-rotating outer sleeve is treated as an equivalent mass block attached to the drive shaft where the upper and lower sliding bearings are located. Specifically:

[0184]

[0185] Where, m n The mass of the non-rotating sliding sleeve is expressed in kg and m. u The equivalent mass of the upper sliding bearing is kg; A u Let m be the cross-sectional area of ​​the upper sliding bearing. 2 ;l u The length of the upper sliding bearing is in meters (m). d The equivalent mass of the lower sliding bearing is kg; A d Let m be the cross-sectional area of ​​the lower sliding bearing. 2 ;l d ρ is the length of the lower sliding bearing, in meters; ρ is the density of the guide head steel, in kilograms per cubic meter of water. 3 .

[0186] In one embodiment, the rib-push force boundary is a unique feature of static push-type rotary steering compared to other rotary steering systems. The rib-push force refers to the lateral cutting force applied to the drill bit during drilling by pushing against the well wall with retractable ribs, thereby achieving real-time guidance during rotary drilling. The guiding force can be equivalently represented by two concentrated forces of constant magnitude and direction acting at the upper and lower sliding bearings, specifically:

[0187]

[0188] Among them, F steer For the rib thrust, N; f u The guiding force at the upper sliding bearing is N; f d The guiding force at the lower sliding bearing is N; n The length of the non-rotating outer jacket is in meters (m); l s1 The distance from the point of action of the rib to the upper sliding bearing is in meters (m); l s2 The distance from the point of action of the rib to the lower sliding bearing is in meters (m); l u The length of the upper sliding bearing is in meters (m); l d Let be the length of the lower sliding bearing, in meters (m).

[0189] When the guiding force acts on the upper and lower sliding bearings, it will generate an additional torque, specifically:

[0190]

[0191] Among them, M u The torque at the upper sliding bearing is N·m; r u M is the radius of the male axis of the upper sliding bearing, in meters. d The torque at the lower sliding bearing is N·m; r d Let be the radius of the male axis of the lower sliding bearing, in meters (m).

[0192] In one embodiment, the initial deformation treatment of the drill string in a curved wellbore involves the initial deformation of the rotary guide bottom drill string due to the constraint of the curved wellbore. This deformation occurs as the drill string changes from a straight state to a curved state coinciding with the wellbore axis. For the bottom drill string, discrete as beam elements, the initial deformation under the constraint of the curved wellbore can be represented by applying initial displacements at the beam element nodes (e.g., ...). Figure 7 As shown), the straight drill string can be processed into a shape that coincides with the wellbore axis. The initial displacement at any beam element node is as follows:

[0193]

[0194] Where N is the north-south coordinate of the well trajectory, in meters; E is the east-west coordinate of the well trajectory, in meters; D is the vertical depth of the well trajectory, in meters; s is the well depth of the well trajectory, in meters; and α is the inclination angle, in degrees. θ is the azimuth angle, °; i is the node number of the beam element; l e , where is the length of the lowest beam element, in meters.

[0195] This invention, based on the unique tool structure and working characteristics of static push-type rotary steerable drilling systems, treats all modules except the bottom drill string body structure as boundary conditions and proposes eight targeted boundary condition processing rules. Existing technologies (such as the study on the mechanical properties and drilling trends of static push-type rotary steerable drilling systems BHA) lack top drive boundaries, drill pipe equivalent boundaries, and non-rotating outer casing boundaries. Furthermore, the drill string-wellbore contact boundaries and drill bit equivalent boundaries they provide also have certain deficiencies. This invention supplements and corrects these deficiencies.

[0196] like Figure 1 As shown, in step S4, a dynamic model of the rotary steerable bottom drill string is constructed based on the overall dynamic equation and boundary condition processing rules, and the dynamic characteristics at any position of the bottom drill string are solved. In one embodiment, the dynamic characteristics include, but are not limited to, dynamic load spectrum, stress spectrum, strain spectrum, displacement spectrum, and acceleration spectrum.

[0197] In one embodiment, a dynamic model of the rotary steerable bottom drill string is constructed based on the overall dynamic equation (Formula 24) and eight boundary condition handling rules.

[0198] In one embodiment, the dynamic model of the rotary steered bottom drill string is solved using the HHT-α implicit method with second-order accuracy. At any time, the overall dynamic equation of the body structure is rewritten according to the HHT-α recursive formula as follows:

[0199]

[0200] Where [M] is the global mass matrix; [K] is the global stiffness matrix; [C] is the global damping matrix; {F} is the global external force vector; t is time, s; Δt is the minimum time interval, s; {q t+Δt} represents the displacement at time t + Δt; The velocity at time t+Δt; Let q be the acceleration at time t+Δt; t} represents the displacement at time t; Let α be the velocity at time t; h These are the damping control parameters.

[0201] Displacement, velocity, and acceleration all require the following specific recursive formulas:

[0202]

[0203]

[0204]

[0205] Compared with the Newmark method used in the prior art, the HHT-α method used in this invention has advantages in coefficient β. h and γ h The value of α was added. h When α h When α = 0, the HHT-α method is equivalent to the Newmark method. In this invention, this parameter α... h The introduction of this feature enables the aforementioned recursive scheme to control algorithm damping. For low-frequency components, the damping increases quite slowly; for high-frequency components, the damping increases more rapidly. Therefore, a small amount of algorithm damping can effectively suppress high-frequency noise while having virtually no impact on the low-frequency solution. Specifically:

[0206]

[0207] By establishing and solving the dynamic model of a static push-type rotary steered bottom drill string, the lateral vibration and vortex phenomena of the rotary steered bottom drill string under different drilling parameters, different drill string combinations, and different wellbore parameters can be analyzed (e.g., Figure 8 Torsional vibration and stick-slip phenomena (such as) Figure 9 Longitudinal vibration and drill skipping phenomena (such as...) Figure 10), the motion stability and guiding capability of rotary guides (e.g.) Figure 11 The dynamic problems such as fatigue stress of the bottom drilling tool were studied.

[0208] The dynamic analysis method for a static push-type rotary steerable drilling system provided by this invention is based on the following assumptions: the inner wall of the wellbore is a continuous and uniform rigid cylinder; the influence of the drill string joint is ignored, and the drill string is regarded as a slender elastic beam with uniform geometric features and material properties, and its deformation is always within the linear elastic range; the contact is considered to be discontinuous, and the contact points are assumed to be located at the larger outer diameter of the downhole tool and at the middle and both ends of the drill string; the intermediate process of elastic deformation and recovery of the wellbore is ignored in the contact model, and the contact is regarded as an instantaneous process, and it is assumed that there is no energy loss in the collision.

[0209] In summary, this invention discretizes the static push-type rotary steerable drilling system into five modules based on its actual functions. This modular modeling approach improves the efficiency of drill string modeling and boundary condition handling. By analyzing the working principles and structural characteristics of different modules, and comprehensively utilizing the theoretical advantages of beam theory, rotor dynamics, and finite element simulation methods, the real static push-type rotary steerable drilling system is theorized into a set of three-dimensional beam element finite element dynamic equations based on Lagrange equations and eight boundary conditions that reflect real working conditions. The HHT-α implicit method is then used for solving these equations, forming a complete dynamic analysis method for the static push-type rotary steerable drilling system. This method can accurately, efficiently, and cost-effectively predict and analyze the safety of rotary steerable drill strings before and after drilling, laying a theoretical foundation for the development of a data-driven virtual simulation system for the dynamic characteristics of static push-type rotary steerable drilling.

[0210] The static push-type rotary steerable drilling system dynamic analysis method provided by this invention can also be used in conjunction with a computer-readable storage medium. The storage medium stores a computer program, which is executed to run the static push-type rotary steerable drilling system dynamic analysis method. The computer program can execute computer instructions, which include computer program code. The computer program code can be in the form of source code, object code, executable file, or some intermediate form.

[0211] Computer-readable storage media can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0212] It should be noted that the contents of computer-readable storage media may be appropriately added to or subtracted from the contents according to the requirements of legislation and patent practice in a jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable storage media may not include electrical carrier signals and telecommunication signals.

[0213] To address the problems of existing technologies, this invention proposes a static push-type rotary steerable bottom drill string dynamics analysis method, which solves the following four problems: First, to consider the actual rotary drilling state of the rotary steerable system, this invention conducts dynamic theoretical modeling research rather than static research. Second, due to the contact nonlinearity and geometric nonlinearity of drill string dynamics, the solution is difficult and inefficient. Therefore, this invention proposes a modular approach to the rotary steerable drilling system. Without affecting the key research object (bottom drill string module), equivalent processing of the corresponding working characteristics of the top drive module, drill pipe module, drill bit module, and wellbore module is performed to simplify calculations and improve efficiency. Third, due to the special structure and working principle of the static push-type rotary steerable drilling system, especially the complex mechanical structure of the steerable head such as the drive shaft, non-rotating outer sleeve, and ribs, this invention proposes eight targeted boundary condition processing methods based on its working principle and characteristics, effectively improving the modeling accuracy. Existing technologies have not deeply explored its tool structure and principles. Fourth, the dynamics study of rotary steerable drilling systems is actually an analysis process of the transformation and dissipation of internal energy within the system. The dynamics solution methods, such as the show method and the low-precision implicit solution method, are difficult to control the energy dissipation problem, leading to deviations in some calculation results. Therefore, the second-order precision HHT-α implicit solution method is adopted, which has good characteristics of controlling damping dissipation and improving the solution accuracy.

[0214] In summary, this invention provides a dynamic analysis method for a static push-type rotary steerable drilling system. It considers the actual dynamic working conditions of the rotary steerable system, improving calculation accuracy, and also performs targeted equivalent processing, improving calculation efficiency. This invention provides a bottom drill string dynamics modeling method and boundary condition processing method that considers the actual working state and structural characteristics of the static push-type rotary steerable system. It employs a second-order accuracy HHT-α implicit method for solution, enabling accurate, efficient, and low-cost pre-drilling prediction and post-drilling analysis of the bottom drill string safety of the rotary steerable system. This lays the theoretical foundation for the development of a data-driven virtual simulation system for the dynamic characteristics of static push-type rotary steerable systems.

[0215] It should be understood that the embodiments disclosed herein are not limited to the specific structures, processing steps, or materials disclosed herein, but should be extended to equivalent substitutions of these features as understood by those skilled in the art. It should also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting.

[0216] In the description of this invention, unless otherwise stated, "a plurality of" means two or more; the terms "upper," "lower," "left," "right," "inner," "outer," "front end," "rear end," "head," "tail," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0217] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0218] The phrase "an embodiment" or "an embodiment" used in this specification means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Therefore, the phrase "an embodiment" or "an embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.

[0219] The embodiments of the present invention are given for illustrative and descriptive purposes only, and are not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles and practical application of the invention, and to enable those skilled in the art to understand the invention and to design various embodiments with various modifications suitable for a particular purpose.

[0220] While the embodiments disclosed in this invention are as described above, the content is merely for the purpose of facilitating understanding of the invention and is not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and variations in form and detail of the implementation without departing from the spirit and scope disclosed herein; however, the scope of patent protection for this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A dynamic analysis method for a static push-type rotary steerable drilling system, characterized in that, The method includes: Based on the mechanical characteristics of the static push-type rotary steerable drilling system, the static push-type rotary steerable drilling system is modularized to construct multiple modules; Taking the rigidly connected body structure in the rotary steerable bottom drill string as the research object, the overall dynamic equation of the body structure is established. Based on the tool structure and working characteristics of the static push-type rotary steerable drilling system, all modules except the main body structure are treated as boundary conditions, and targeted boundary condition processing rules are proposed. These boundary condition processing rules include: drill string... Wellbore contact boundary, top drive boundary, drill pipe equivalent boundary, bottom drill string upper boundary, drill bit equivalent boundary, non-rotating outer sleeve equivalent boundary, wing rib pushing force boundary, and initial deformation treatment of drill string in curved wellbore. Based on the overall dynamic equation and the boundary condition processing rules, a dynamic model of the rotary steerable bottom drill string is constructed, and the dynamic characteristics at any position of the bottom drill string are solved.

2. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 1, characterized in that, The module includes, but is not limited to: top drive module, drill pipe module, bottom drill string module, drill bit module, and wellbore module. The bottom drill string module includes various instruments, upper drill collars, and weighted drill pipes in the static push-type rotary steerable drilling system. The wellbore module is the wellbore trajectory formed by the drilling of the static push-type rotary steerable drilling system.

3. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 1, characterized in that, The overall dynamic equations of the aforementioned body structure are established through the following steps: Three Cartesian coordinate systems were established: the wellhead coordinate system, the wellbore coordinate system, and the unit local coordinate system. Based on the typical drill string structure of the static push-type rotary steerable drilling system, the main body structure is processed into a three-dimensional elastic beam with a variable cross section. The three-dimensional elastic beam is discretized at key locations using the finite element method and divided into Timoshenko beam elements with multiple nodes and degrees of freedom that can consider shear deformation. The expressions for the kinetic energy, potential energy, and generalized force of the beam element are derived. Substituting these expressions into the Lagrange equations, the finite element dynamic equations of the beam element are derived. By combining the finite element dynamic equations corresponding to all beam elements, the overall dynamic equations of the body structure are obtained.

4. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 3, characterized in that, The wellhead coordinate system, with the wellhead position as the origin and north, east, and vertical depth as the coordinate axes, is used to describe the wellbore trajectory. The wellbore coordinate system, with any node on the wellbore axis as the origin and the axis tangent, wellbore elevation, and torsional azimuth as the coordinate axes, is used to describe the position and deformation of the bottom drill string. The local coordinate system, with any node on the drill string axis as the origin and the drill string axis and drill string cross-section as the three coordinate axes, is used to describe the torsion of the bottom drill string axis.

5. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 3, characterized in that, The key locations include, but are not limited to: the instrument end face, the variable cross-section location, and the location where the pushing force is applied.

6. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 3, characterized in that, The three-dimensional elastic beam is discretized at the key locations using the finite element method, and divided into multiple Timoshenko beam elements with 2 nodes and 12 degrees of freedom, considering shear deformation. The nodal displacement vectors of the beam elements are expressed as: in, q e The displacement vector of the beam element nodes; u z , u x , u y Let Z represent the nodal displacements of the beam element along the Z, X, and Y axes of the wellbore coordinate system, in meters. Let be the rotation angle of the beam element node relative to the Z, X, Y axes of the local coordinate system, in rad; i and j The node numbering for the beam element.

7. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 3, characterized in that, The overall dynamic equation of the body structure is expressed as: in, q For generalized variables; M [ is the global quality matrix;] K [ is the global stiffness matrix;] C ] is the global damping matrix; { F } represents the global external force vector.

8. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 1, characterized in that, The boundary condition processing rules include the drill string-wellbore contact boundary. Using the method for handling disk rotors and external constraints in rotor dynamics, a massless disk rotor is added at a preset contact point. A constant contact stiffness is used to describe the contact force between the drill string and the wellbore. Specifically: in, F n The contact force is N; χ The distance between the drill string and the wellbore is expressed in meters (m). K c The contact stiffness is expressed in N / m, and is the equivalent stiffness coefficient between the drill string and the wellbore rock.

9. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 3, characterized in that, The boundary condition processing rules include the top drive boundary. The top drive hinges the upper end of the drill string at the center of the wellhead and rotates the drill string clockwise at a fixed rotational speed. Therefore, the top drive boundary has three degrees of freedom constrained, with the circumferential direction constrained by a fixed clockwise rotational speed. Specifically: in, u z , u x , u y These are the nodal displacements of the beam element in the wellbore coordinate system, in meters; Let be the circumferential rotation angle of the beam element node, in rad; ω 0 represents the top drive speed, in r / min.

10. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 2, characterized in that, The boundary condition processing rules include the drill pipe equivalent boundary, which treats the drill pipe module as a torsion spring to connect the top drive and the bottom drill string, thereby transmitting rotational speed and torque. Specifically: in, k t The equivalent torsional stiffness of the drill pipe is given in N·m. L p The drill pipe length is in meters (m). G Shear modulus, Pa; I z Let m be the polar moment of inertia of the beam element. 4 .

11. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 3, characterized in that, The boundary condition processing rules include the upper boundary of the bottom drill string, where the upper end of the bottom drill string is hinged at the center of the wellbore, thus constraining three degrees of displacement freedom, specifically: in, u z , u x , u y These are the nodal displacements of the beam element in the wellbore coordinate system, in meters.

12. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 3, characterized in that, The boundary condition processing rules include the drill bit equivalent boundary. The lower end of the bottom drill string contacts the formation through the drill bit and is subject to wellbore constraints and the reverse drilling pressure and torque from the formation. The drill bit is considered as a full-width boundary, meaning that the two lateral displacement degrees of freedom of the drill bit node are constrained, specifically: in, u x , u y These are the nodal displacements of the beam element in the wellbore coordinate system, in meters; L b The length of the bottom drill string is in meters (m). During rock breaking, the drilling pressure fluctuates with the torsion of the drill bit. The drilling pressure can be treated as a sinusoidal function that varies with the drill bit rotation angle, specifically: in, W b The actual drilling pressure at the drill bit, in N; W 0 represents the steady-state amplitude of drilling pressure, N; The amplitude of drilling pressure fluctuation is related to the degree of longitudinal vibration of the drill bit. n As a motivating factor; The drill bit rotation angle is expressed in rad. The magnitude of the drill bit counter-torque can be categorized into three cases based on the drill bit's motion state and the active torque applied by the drill string: viscous phase, viscous-to-slip transition, and slip phase, specifically: in, T b The actual torque at the drill bit is expressed in N·m. G Shear modulus, Pa; I z Let m be the polar moment of inertia of the beam element. 4 ; l e The length of the lowest beam element is in meters (m). The circumferential rotation angle of the drill bit node is expressed in rad. Let radii be the circumferential rotation angle of a node on the drill bit, expressed in rad. ω b The drill bit rotation speed is r / min; δ The critical speed for the viscous phase is given in r / min. r b Let be the outer diameter of the drill bit, in meters (m). μ s The coefficient of static friction; μ k The coefficient of kinetic friction; d c The attenuation coefficient; γ eq It represents the slip ratio.

13. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 1, characterized in that, The boundary condition processing rules include the equivalent boundary of the non-rotating outer sleeve. The non-rotating outer sleeve is supported on the drive shaft by two sliding bearings, and is non-rigidly connected to the drive shaft. It is a non-rotating structure independent of the rotary guide bottom drill bit. The non-rotating outer sleeve is processed as an equivalent mass block attached to the drive shaft where the upper and lower sliding bearings are located, specifically: in, m n The mass of the non-rotating sliding sleeve is in kg. m u The equivalent mass of the upper sliding bearing is kg; A u Let m be the cross-sectional area of ​​the upper sliding bearing. 2 ; l u The length of the upper sliding bearing is in meters (m). m d The equivalent mass of the lower sliding bearing is kg; A d Let m be the cross-sectional area of ​​the lower sliding bearing. 2 ; l d The length of the lower sliding bearing is in meters (m). ρ Density of guide head steel, kg / m 3 .

14. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 1, characterized in that, The boundary condition processing rules include the rib pushing force boundary. The rib pushing force refers to the lateral cutting force applied to the drill bit by pushing against the well wall through retractable ribs during drilling, thereby achieving real-time guidance during rotary drilling. The guiding force can be equivalent to two concentrated forces of constant magnitude and direction acting on the upper and lower sliding bearings, specifically: in, F steer The thrust force of the ribs is N; f u The guiding force at the upper sliding bearing is N; f d The guiding force at the lower sliding bearing is N; l n The length of the non-rotating outer jacket is in meters. l s1 The distance from the point of action of the rib to the upper sliding bearing is in meters (m). l s2 The distance from the point of action of the rib to the lower sliding bearing is in meters (m). l u The length of the upper sliding bearing is in meters (m). l d The length of the lower sliding bearing is in meters (m). When the guiding force acts on the upper and lower sliding bearings, it will generate an additional torque, specifically: in, M u The torque at the upper sliding bearing is N·m; r u Let the radius of the male axis of the upper sliding bearing be m; M d The torque at the lower sliding bearing is N·m; r d Let be the radius of the male axis of the lower sliding bearing, in meters (m).

15. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 3, characterized in that, The boundary condition processing rules include the initial deformation processing of the drill string in the curved wellbore. Due to the constraint of the curved wellbore, the rotary guide bottom drill string will undergo initial deformation, that is, the drill string changes from a straight state to a curved state coinciding with the wellbore axis. For the bottom drill string discrete as beam elements, the initial deformation of the bottom drill string under the constraint of the curved wellbore can be represented by applying an initial displacement at the beam element node, which can process the straight drill string into a shape coinciding with the wellbore axis. The specific initial displacement at any beam element node is as follows: in, N Let be the north-south coordinates of the wellbore trajectory, in meters (m). E Let M be the east-west coordinate of the wellbore trajectory, in meters (m). D Let m be the vertical depth of the wellbore trajectory; s Let m be the depth of the wellbore trajectory; α The inclination angle is °; The azimuth angle is in degrees. i Number the nodes of the beam element; , where is the length of the lowest beam element, in meters.

16. The dynamic analysis method for a static push-type rotary steerable drilling system as described in claim 1, characterized in that, The dynamic model of the rotary steerable bottom drill string is solved using the HHT-α implicit method with second-order accuracy. At any time, the overall dynamic equation of the main structure is rewritten according to the HHT-α recursive formula as follows: in,[ M [ is the global quality matrix;] K [ is the global stiffness matrix;] C ] is the global damping matrix; { F } represents the global external force vector; For time, s; △ The minimum time interval is s; for t +△ t Displacement at any moment; for t +△ t Speed ​​in a given moment; for t +△ t Constant acceleration; for t Displacement at any moment; for t Speed ​​in a given moment; These are the damping control parameters.

17. A dynamic analysis method for a static push-type rotary steerable drilling system as described in any one of claims 1-16, characterized in that, The dynamic characteristics include, but are not limited to, dynamic load spectrum, stress spectrum, strain spectrum, displacement spectrum, and acceleration spectrum.

18. A storage medium, characterized in that, It includes a series of instructions for performing the method steps as described in any one of claims 1-17.

Images