CN113065211B - Fatigue life prediction method for bottom hole assembly based on drill string dynamics - Google Patents
Fatigue life prediction method for bottom hole assembly based on drill string dynamics Download PDFInfo
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Abstract
The invention discloses a drilling string dynamics-based bottom hole assembly fatigue life prediction method, which relates to the technical field of oil and gas development and comprises the following steps: s1: establishing a coordinate axis to obtain a displacement vector form of the bottom hole assembly of each unit; s2: obtaining a drill column dynamic model according to a Lagrange equation; s3: obtaining a stress model when the drilling tool assembly is in contact with a well wall; s4: discretely solving a drill string dynamic model of each unit, and obtaining the equivalent stress of the bottom hole assembly according to the stress model; s5: obtaining a fatigue life of the bottom hole assembly. The invention considers the dynamic vibration characteristic of the bottom drilling tool assembly in a load state, establishes a fatigue life prediction model of the bottom drilling tool assembly based on drill string dynamics, and ensures that the fatigue life prediction effectiveness obtained by calculation is better.
Description
Technical Field
The invention relates to the technical field of petroleum and natural gas development, in particular to a method for predicting the fatigue life of a bottom drilling tool assembly based on drill string dynamics.
Background
The lower drill string of the drilling machine is generally composed of a Bottom Hole Assembly (BHA), a weighted drill pipe (HWDP) and drill pipes, wherein the bottom hole assembly refers to the drill string which is 100-500 m away from a drill bit, and the drill string mainly comprises drill collars, the weighted drill pipe and other auxiliary tools. During load operation, the bottom hole assembly is subjected to the combined action of axial and lateral loads, torque, pressure, friction and viscous drag, while also being constrained by the borehole wall.
The bottom hole assembly is the most prone to failure and damage in oil and gas well drilling construction, and the fatigue life and the use strength of the bottom hole assembly limit the process and the construction progress of the drilling construction. Under the conditions of severe working conditions and complex stress, the drilling tool is subjected to abrasion, corrosion and abnormal damage, so that the fracture, puncture and failure of the bottom drilling tool assembly are accelerated, the fatigue life of the bottom drilling tool assembly is difficult to predict under the influence of the working conditions, geological conditions and other factors of the drilling tool, and the fatigue life of the bottom drilling tool assembly is difficult to effectively control in designing a drilling process and a construction process.
In order to solve the above problems, researchers mainly focus on the fatigue life prediction of the bottom hole assembly in two aspects, namely, the drilling tool material and the dynamic characteristics of the drilling tool, and both the two methods are established under the stress assumption that the bottom hole assembly is in one or more equilibrium states when predicting the fatigue life of the bottom hole assembly at present. However, in the process of the load operation of the bottom hole assembly, the bottom hole assembly is in a motion state at all times, the motion state of the bottom hole assembly changes at all times, and the force applied to the bottom hole assembly changes at all times, so that the fatigue life prediction by adopting a stable and balanced state is difficult to ensure the effectiveness of the result, and the fatigue life prediction is possibly far away from the actual load condition of the bottom hole assembly.
Disclosure of Invention
The method aims to solve the problem that the result effectiveness of a method for predicting the fatigue life of a bottom hole assembly in the prior art is not high, and provides a method for predicting the fatigue life of the bottom hole assembly based on drill string dynamics.
In order to achieve the above object, the present application provides the following technical solutions: the method for predicting the fatigue life of the bottom hole assembly based on drill string dynamics comprises the following steps:
s1: dividing a bottom hole assembly of a target well into a plurality of units along a borehole axis, establishing coordinate axes by taking the borehole axis direction of the target well as a Z axis, a righteast direction as an X axis and a rightsouth direction as a Y axis, and obtaining a bottom hole assembly displacement vector equation of each unit;
s2: obtaining a drill string dynamics model of the bottom hole assembly according to a Lagrange equation;
s3: assuming that the target well wall is rigid, and the bottom hole assembly is randomly contacted with the target well wall, and obtaining a stress model when the bottom hole assembly is contacted with the well wall;
s4: setting the bottom hole assembly and boundary conditions, substituting the displacement vector equation of the bottom hole assembly into the drill string dynamic model, discretely solving the drill string dynamic model of each unit, and obtaining the equivalent stress of the bottom hole assembly according to the stress model;
s5: setting initial conditions of the bottom hole assembly, and obtaining the fatigue life of the bottom hole assembly according to the Walker model and the equivalent stress of the bottom hole assembly.
Further, the equation for the bottom hole assembly displacement vector of each of the units is:
U＝(Ux1 Uy1 Uz1 θx1 θy1 θz1 Ux2 Uy2 Uz2 θx2 θy2 θz2)T；
wherein, Ux1、Uy1、Uz1、Ux2、Uy2、Uz2Respectively linear displacement of each unit in each direction of two nodes; thetax1、θy1、θz1、θx2、θy2、θz2The angular displacement of two nodes for each unit.
Further, the drill string dynamics model of the bottom hole assembly is:
wherein,
{ U }, { F } are generalized acceleration, generalized velocity, generalized displacement and generalized external force vector, respectively; [ M ] A],[C],[K]Respectively a mass matrix, a damping matrix and a stiffness matrix.
Further, the generalized external force vector includes a centrifugal force and a gravity applied to two nodes of each of the units, and thus the matrix of the generalized external force vector is a 12-dimensional matrix.
Further, the stress model when the bottom hole assembly is in contact with the well wall is as follows:
wherein, FezIs axial frictional resistance, FerIs tangential frictional resistance, TeFor borehole wall torque, MeIs a bending moment; mu.seThe friction coefficient of the bottom drilling tool assembly and the well wall; diIs the wellbore diameter, m; fNContact force, N.
Further, the boundary conditions of the bottom hole assembly include an upper boundary condition and a lower boundary condition, where the upper boundary condition is a stress condition of the bottom hole assembly at the wellhead of the target well, and the upper boundary condition specifically includes:
Ux＝0,UY＝0,UZ＝0,θz＝Ωt,θx＝0,θy＝0；
wherein, Ux、Uy、UzRespectively the displacement of the bottom drilling tool assembly at the wellhead; thetax、θy、θzRespectively the rotation angles of the bottom drilling tool assembly at the wellhead around each coordinate axis; omega is the rotating speed of the bottom drilling tool assembly, rad/s; t represents time, s.
The lower boundary condition is the stress condition of the bottom hole assembly at the wellhead of the target well; the method comprises the following steps:
wherein, P0The amplitude of the exciting force is a constant given by well site data, KN; dbRepresents the bit diameter, m; n represents the rotating speed of the rotating disc; h represents the depth of cut, m, of one rotation of the drill bit; mu.sbRepresenting the coefficient of friction of the drill bit with the bottom of the well; t represents time, s; pwobRepresents the bottom hole weight on bit, KN; ω represents the rotational angular velocity of the drill, rad/s; WOB represents the combined force at the bottom of the well, KN; t ispRepresenting the torque, N · m, on the bottom hole assembly due to the interaction of the bit with the bottom hole.
Further, in step S4, the dynamic model is discretely solved by a generalized- α method.
Further, the drill string dynamics model solution specifically comprises the steps of:
s41: obtaining a general calculation formula of the generalized-alpha method according to the basic form of the generalized-alpha method;
s42: establishing a null matrix of a stiffness matrix [ K ], a mass matrix [ M ] and a damping matrix [ C ] and substituting the null matrix into a general calculation formula of a generalized-alpha method;
s43: assignment d0And v0And a obtained according to the basic form of the generalized-alpha method0A value;
s44: setting a time step length and a limit spectrum radius, and calculating a required integral constant;
s45: calculating to obtain an effective stiffness matrix, an effective load vector, displacement at the moment t + delta t, acceleration at the moment t + delta t and speed at the moment t + delta t;
s46: and (5) bringing the values obtained in the step (S45) into the drill string dynamic model, and performing iterative calculation to obtain time functions of model displacement, speed and acceleration.
Further, the prediction method is also based on the following assumptions:
the well bore is circular, the axis of the well bore is coincident with the axis of the bottom hole assembly under the initial condition, and no annular gap exists between the drill bit and the well wall;
the bottom hole assembly deforms to negligible micro deformation regardless of shear stress;
the effects of the bottom hole assembly sub and the threaded bore slots are not considered.
Compared with the prior art, the invention has the following beneficial effects: the invention discloses a method for predicting the fatigue life of a bottom drilling tool assembly based on drill string dynamics, which comprises the steps of establishing a drill string dynamic model according to a Lagrange equation, fully considering the stress condition and the displacement condition of the bottom drilling tool assembly under the actual load condition, utilizing a generalized-alpha method to carry out discrete solution on the drill string dynamic model, combining a fourth strength theory to obtain the equivalent stress of the bottom drilling tool assembly, and further calculating according to a Walker model to predict the fatigue life of the bottom drilling tool assembly. The method for predicting the fatigue life of the bottom hole assembly considers the displacement of the bottom hole assembly and the collision with the well wall when the bottom hole assembly works under load, obtains a dynamic model of the bottom hole assembly in the load process, has few assumed conditions, better accords with the actual condition of the bottom hole assembly when the bottom hole assembly works under load, improves the accuracy of the predicted fatigue life of the bottom hole assembly, and is beneficial to the reference and guidance of the prediction result on the bottom hole assembly in the construction and application processes.
Drawings
FIG. 1 is a schematic flow chart of a method for predicting the fatigue life of a bottom hole assembly based on drill string dynamics in accordance with the present disclosure;
FIG. 2 is a schematic diagram of coordinates of two nodes of a unit in the method for predicting the fatigue life of a bottom hole assembly based on drill string dynamics disclosed by the invention;
FIG. 3 illustrates a gravity model for each unit of the drill string dynamics bottom hole assembly fatigue life prediction method disclosed herein;
FIG. 4 illustrates a model of contact between the bottom hole assembly and the borehole wall in a drill string dynamics bottom hole assembly fatigue life prediction method disclosed herein;
FIG. 5 is a graph illustrating acceleration at a node on a bottom hole assembly according to some embodiments of the present disclosure;
FIG. 6 is a graph illustrating equivalent stress at a node on a bottom hole assembly according to some embodiments of the present disclosure;
FIGS. 7 to 13 show a mass matrix, a gyro damping matrix, a stiffness matrix and a non-stiffness matrix in the drill string dynamics bottom hole assembly fatigue life prediction method disclosed by the invention.
Detailed Description
The present invention will be described in further detail with reference to test examples and specific embodiments. It should be understood that the scope of the above-described subject matter is not limited to the following examples, and any techniques implemented based on the disclosure of the present invention are within the scope of the present invention.
In the prior art, researchers mainly focus on two aspects of fatigue life prediction of a bottom hole assembly, namely drilling tool materials and the dynamic characteristics of the drilling tool, and the two methods are established under the stress assumption condition that the bottom hole assembly is in one or more equilibrium states when predicting the fatigue life of the bottom hole assembly at present. However, in the process of the load operation of the bottom hole assembly, the bottom hole assembly is in a motion state at all times, the motion state of the bottom hole assembly changes at all times, and the force applied to the bottom hole assembly changes at all times, so that the fatigue life prediction by adopting a stable and balanced state is difficult to ensure the effectiveness of the result, and the fatigue life prediction is possibly far away from the actual load condition of the bottom hole assembly.
In view of the above technical problems, referring to fig. 1, the present application discloses a method for predicting the fatigue life of a bottom hole assembly based on drill string dynamics, comprising the following steps:
s1: dividing a bottom hole assembly of a target well into a plurality of units along a borehole axis, establishing coordinate axes by taking the borehole axis direction of the target well as a Z axis, a righteast direction as an X axis and a rightsouth direction as a Y axis, and obtaining a bottom hole assembly displacement vector equation of each unit;
s2: obtaining a drill string dynamics model of the bottom hole assembly according to a Lagrange equation;
s3: assuming that the target well wall is rigid, and the bottom hole assembly is randomly contacted with the target well wall, and obtaining a stress model when the bottom hole assembly is contacted with the well wall;
s4: setting the bottom hole assembly and boundary conditions, substituting the displacement vector equation of the bottom hole assembly into the drill string dynamic model, discretely solving the drill string dynamic model of each unit, and obtaining the equivalent stress of the bottom hole assembly according to the stress model;
s5: setting initial conditions of the bottom hole assembly, and obtaining the fatigue life of the bottom hole assembly according to the Walker model and the equivalent stress of the bottom hole assembly.
It should be noted that the bottom hole assembly has an ultra-long aspect ratio characteristic, and is in a long and narrow space filled with drilling fluid or gas to make a rotary motion, and bears the actions of complex loads such as tension, compression, bending, torsion, internal and external hydraulic pressure, and the like, so that the dynamic analysis of the bottom hole assembly is a very complex problem. In order to implement the fatigue life prediction method of the bottom hole assembly, in addition to the assumption in step S3, the following assumptions are made in the present document:
(1) the well hole is circular, the axis of the well hole is superposed with the axis of the bottom drilling assembly under the initial condition, and no annular gap exists between the drill bit and the well wall.
(2) Neglecting shear stress, the bottom hole assembly deforms to negligible minor deformation.
(3) Neglecting the influence of the bottom hole assembly joint, the thread hole groove and the like.
In the assumption (2), the assumption of the slight deformation means that the slight deformation is a case when the deformation amount of the member due to the external force is much smaller than the original size. This allows the calculation to be simplified by assuming that the component deformation can be ignored and the analysis is performed on its original size.
It should be noted that, referring to fig. 2, in step S1, the bottom hole assembly is divided into a plurality of units, each unit includes two nodes, and a coordinate system is established at the two nodes, so that the equation of the displacement vector of the bottom hole assembly of the unit can be obtained as follows:
U＝(Ux1 Uy1 Uz1 θx1 θy1 θz1 Ux2 Uy2 Uz2 θx2 θy2 θz2)T (1)；
wherein x is1、x2、y1、y2、z1、z2Coordinates of two nodes of each unit respectively; t is kinetic energy; u shapex1、Uy1、Uz1、Ux2、Uy2、Uz2Respectively displacement of each unit in each direction of two nodes; thetax1、θy1、θz1、θx2、θy2、θz2The rotation angles of the two nodes of each unit rotating around the coordinate axis are respectively.
It should be noted that, in the step S2, the lagrangian equation is:
in the formula, T represents kinetic energy; v represents potential energy;
representing a velocity vector; f represents an external force vector; u represents the amount of displacement.
The drill string dynamics model obtained is as follows:
in the formula,
{ U }, { F } are generalized acceleration, velocity, displacement, and force vectors, respectively. [ M ] A],[C],[K]Respectively a mass matrix, a damping matrix and a stiffness matrix.
It should be noted that during the operation of loading the bottom hole assembly, the motion thereof mainly includes the lateral translational motion and the rotation, so that the kinetic energy of each unit includes the translational kinetic energy and the rotational kinetic energy, and therefore, the kinetic energy of each unit can be expressed as:
in the formula, ρdIs the density of the drill string material;
is the modulo length of vector e; r isPThe modular length of the displacement vector of any point on the drill string; dtIs a form of a shape function; the right end of the equation (4) contains four terms, and the first term represents the kinetic energy of particle translation of the unit; the second term and the third term are coupled terms of particle translation and rotation, and are zero because the calculation of the inertia moment depends on the centroid of the cross section; the fourth term represents the rotational kinetic energy of the unit particles, including the gyroscopic moment term.
Formula (4) can be obtained by the following steps:
in the coordinate system, the position of any point P on the bottom hole assembly can be expressed as:
in the formula,
is a vector of displacement of the P-axis,
the components of the P point displacement vector on the x, y and z axes are shown.
The time is derived to obtain the velocity expression for point P:
in the formula,
the velocity vector, matrix [ omega ], representing P]Is a third-order antisymmetric matrix related to omega]It can be expressed as:
vector in formula (1) by finite element method
Can be expressed as:
in the formula, D is a shape function,
as the amount of displacement within the cell, is,
according to the displacement field assumed by the shape function, the translation of the cell in three directions can be expressed as:
the cross-sectional rotation can be expressed as:
the torsional displacement of the cross-section can be expressed as:
substitution of formula (6) can yield:
at this time, the whole unit is integrated to obtain formula (3):
further simplification of formula (3) yields:
in the formula, MtTranslating the mass matrix for the cell;
is a cell twist mass matrix; mrRotating an inertial mass matrix for the unit; meIs a torsional and transverse inertia coupling mass matrix; gtA gyro matrix;
is the constant angular velocity of the drill assembly; j is the moment of inertia about the axis.
Wherein the potential energy of each unit can be expressed as:
wherein E is the modulus of elasticity, Pa, of the bottom hole assembly; g is the shear modulus of the bottom hole assembly, Pa.
Formula (13) can be obtained by: elastic potential energy, also called strain energy, passing through stress sigmaijAnd strain epsilonijIt is given.
Because of the symmetrical relationship of stress and strain, the stress and strain can be expressed by six quantities respectively.
From Hooke's law, sigma ═ Chε, wherein
In the formula,
mu is Poisson's ratio, G is shear modulus, MPa.
The strain energy per unit volume can be expressed as:
due to sigma2＝σ3＝σ 50. Substitution of formula (15) to epsilon2＝ε3＝-με1And ε 50, so equation (16) can be simplified as:
according to the green strain equation, the displacement strain relationship can be written as:
considering the axial load, bending moment and torque induced displacement and also the assumption of independence between them, the displacement field can be expressed as:
in the formula ux、uy、uzIs the displacement of an arbitrary point in a cell, uxo、uyo、uzoIs the displacement of a point on the neutral axis, which is a function of x only. When the beam unit satisfies
When the shear force is applied, the deformation caused by the shear force is less than 5% of the total deformation, and if the deformation is negligible, the following deformation occurs:
substituting the formula (18-20) into the formula (16) to obtain the formula (13).
Using the given shape function, equation (13) can be written in the form of a matrix as follows:
converting the displacement vector e into a generalized displacement vector U;
equation (21) can be simplified as:
similarly, equation (12) can be simplified to the following matrix form:
it should be noted that the generalized external force vector includes the centrifugal force and the gravity applied to two nodes of each unit, and thus the matrix of the generalized external force vector is a 12-dimensional matrix.
As shown in fig. 3, the gravity component of each unit of the bottom hole assembly in each coordinate axis direction is:
wherein q is the equivalent gravity of the bottom hole assembly in unit length and is N/m; alpha is the angle between the axis of the beam element and the vertical.
Thus, the equivalent nodal force of the gravity vector is:
for the cross section of the bottom hole assembly, the center of mass is not completely consistent with the centroid, an unbalanced force (centrifugal force) is generated when the bottom hole assembly rotates,
the centrifugal force generated by the rotation of each unit in the three directions of x, y and z can be expressed as:
wherein β is the phase angle of the center of gravity, rad;
thus, the generalized external force vector can be expressed as:
{F}＝(Fx1 Fy1 Fz1 Mx1 My1 T1 Fx2 Fy2 Fz2 Mx2 My2 T2) (27)
in the formula, Fx1、Fy1、Fz1、Fx2、Fy2、Fz2Axial forces of two nodes of each unit in three coordinate axis directions are respectively; mx1、My1、Mx2、My2Bending moments of two nodes of each unit in the X-axis direction and the Y-axis direction respectively; t is1、T2Respectively the torque.
And (3) driving the formula (22), the formula (23) and the formula (27) into the formula (2), integrating and then representing by using a matrix to obtain the drill string dynamic model of the bottom hole assembly.
It should be noted that the quality matrix can be expressed as:
in the formula, MinRepresenting an additional mass matrix, M, equivalent by the inertial force of the drilling fluidotAnd the equivalent additional mass matrix represents the action force of the drilling fluid on the transverse vibration of the drilling tool component.
It should be noted that the stiffness matrix can be expressed as:
[K]＝[KL]+[KN] (30)
wherein [ K ]L]Represents linear stiffness, [ K ]N]Representing the nonlinear stiffness.
The damping matrix can be expressed as:
[C]＝[CD]+[CN] (31)
[CD]showing Rayleigh damping, [ CN]Representing gyro damping.
[CD]＝αD[M]+βD[KL] (32)
In the formula, alphaD、βDIs a constant.
In step S3, the bottom hole assembly is in substantially random contact with the borehole wall assuming the borehole wall is rigid. Referring to FIG. 4, the force exerted by the borehole wall when the bottom hole assembly is in contact with the borehole wall includes: axial frictional resistance FezTangential frictional resistance FerWell wall torque TeAnd bending moment Me。
Therefore, the stress model when the bottom hole assembly is in contact with the well wall is as follows:
in the formula, mueThe friction coefficient of the bottom drilling tool assembly and the well wall; fNThe pressure applied by the well wall to the bottom hole assembly when the bottom hole assembly contacts the well wall under the load state is disclosed.
In addition, FNCalculated by the following equation:
in the formula (d)iIs the wellbore diameter, m; doIs the diameter of the bottom hole assembly, m; v. ofrIs the radial velocity of the bottom hole assembly, m/s; u. ofrIs the radial displacement of the bottom hole assembly, m; k is a radical ofhIs the stiffness of the wellbore, N/m; v. of1And v2Respectively, the velocities before and after the node collision, m/s.
In step S4, the bottom hole assembly boundary conditions include an upper boundary condition and a lower boundary condition, wherein the upper boundary condition is a force condition of the bottom hole assembly at the target wellhead.
Because during actual drilling operation, produce the restraint in the transverse direction at well head position carousel to the drilling string of bottom hole assembly, the transverse displacement degree of freedom and the rotational degree of freedom of bottom hole assembly node that the Z axle is 0 department in the numerical model corresponding are fixed, do not increase and decrease with time, and the drilling string only receives axial force and moment of torsion effect, therefore the upper portion boundary condition of drilling string is:
Ux＝0,UY＝0,UZ＝0,θz＝Ωt,θx＝0,θy＝0 (35)。
wherein the drill bit at the lower portion of the bottom hole assembly is reamed downhole, with lateral displacement at the drill bit being constrained but rotation about each axis being unconstrained. The bit is also subjected to an excitation force P and a bit torque T resulting from the interaction of the bit with the formationpThus, the drill bit is only subjected to the exciting force P and the drill bit torque TpSo the lower boundary conditions of the bottom hole assembly are:
in the formula, P0The amplitude of the exciting force is a constant given by well site data, KN; dbRepresents the bit diameter, m; n represents the rotating speed of the rotating disc; h represents the depth of cut, m, of one rotation of the drill bit; mu.sbRepresenting the coefficient of friction of the drill bit with the bottom of the well; t represents time, s; pwobRepresents the bottom hole weight on bit, KN; ω represents the rotational angular velocity of the drill, rad/s; WOB represents the combined force at the bottom of the well, KN; t ispRepresenting the torque, N · m, to the drill string due to the interaction of the bit with the bottom hole.
In step S4, the dynamic model is discretely solved by a generalized- α method, which specifically includes the following steps:
s41: obtaining a general calculation formula of the generalized-alpha method according to the basic form of the generalized-alpha method;
s42: establishing a null matrix of a stiffness matrix [ K ], a mass matrix [ M ] and a damping matrix [ C ] and substituting the null matrix into a general calculation formula of a generalized-alpha method;
s43: assignment d0And v0And a obtained according to the basic form of the generalized-alpha method0A value;
s44: setting a time step length and a limit spectrum radius, and calculating a required integral constant;
s45: calculating to obtain an effective stiffness matrix, an effective load vector, displacement at the moment t + delta t, acceleration at the moment t + delta t and speed at the moment t + delta t;
s46: and substituting the values obtained in the S45 into the drill string dynamic model, and performing iterative calculation to obtain the dynamic model.
It should be noted that the generalized- α method has the basic form:
in the formula (d)n、vnAnd anRespectively represent
And U, namely the displacement, the speed and the acceleration of the bottom hole assembly; Δ t represents the time step, s; a subscript n ∈ {0,1,2.. said., R-1 }; r represents the number of time steps.
Wherein alpha isf2,αm2,γ2And beta2The relationship and calculation between them is as follows:
in the formula, ρ∞2Denotes the limiting spectral radius, ρ∞2∈[0,1]。
Taking formula (37) and formula (39) into formula (38) to obtain a general calculation formula of the generalized-alpha method, wherein the general calculation formula of the generalized-alpha method is specifically as follows:
in step S42, the empty matrices of the stiffness matrix [ K ], the mass matrix [ M ], and the damping matrix [ C ] are all 12 × 12 empty matrices.
In addition, d is determined according to the upper boundary condition0And v0The value is assigned to zero and is taken (37), the acceleration in the initial case is obtained: a is0。
In step S44, the integral parameter and its specific calculation formula are:
and an effective stiffness matrix of the bottom hole assembly
Payload vector
The calculation formula of (a) is respectively:
therefore, the displacement, acceleration and velocity of the bottom hole assembly at the time t + Δ t can be obtained from equations (17) to (19) and (25) to (27):
and (5) driving the formula (28) into the formula (8), and performing iterative solution to obtain a dynamic model of the bottom hole assembly.
Because the stress model of the bottom hole assembly contacting the well wall is obtained in step S3, each unit can be regarded as a straight beam with two hinged ends during prediction, and each node is respectively arranged at the left end and the right end of the straight beam unit and is subjected to the axial force Fz1Two transverse bending moments Mx1 My1And the impact force F generated by the action of the drill string and the well wallc、Mx1、My1The function of (1).
From the kinetic model, the axial force F can be obtainedz1、Mx1、My1The specific calculation method is as follows:
Fz1＝KL1Uz1 (48)
wherein E is the modulus of elasticity of the material and is a constant determined by the material of the drill string; i is the moment of inertia of the section of the drill string, the section of the drill string is a circular section, and the expression of the moment of inertia is as follows: (ii) a KL1Linear rigidity corresponding to the node is obtained by a dynamic model; u shapex1、Uy1、
The displacement and the speed of the node are respectively obtained by a dynamic model.
Wherein the impact force FcThe method is obtained according to the momentum theorem, and specifically comprises the following steps:
wherein, the delta Q is the change of the momentum of the drill string unit in the collision process, N.s; Δ t is the time of the collision process, s.
According to formula impact force FcThe stress sigma generated in the contact process of the drill string and the well wall can be obtainedc，σcCalculated by the following formula:
in the formula, AcIs the contact area.
Wherein the contact area can be estimated by the following formula:
Ac＝ζLidwd (51)
in the formula, LiIs the unit length, m. dwdThe contact arc length under dynamic conditions, m. Zeta is the area proportionality coefficient when the drill string collides with the well wall, and the value is 0.003<ζ<0.006。
Stress force analysis is carried out on any node of each unit, and the normal stress of the drill string along the Z-axis direction can be obtained as follows:
in the formula A1Is the cross-sectional area of the drill string at the node point, Ix1Is the moment of inertia of the x-axis, Iy1The moment of inertia of the y-axis.
Furthermore, the first two and three principal stresses of the drill string, which can be obtained from the Moire stress circle, are:
it should be noted that τ is the shear stress to which the node is subjected, and it is generated by the torque, and it should be regarded as a constant to deal with the torque of each node of the vertical well in the practical application process.
According to the fourth strength theory, a calculation formula of the equivalent stress applied to the bottom hole assembly can be obtained, which is as follows:
in the solution of the dynamic model, the displacement, the velocity and the acceleration of the bottom hole assembly are obtained, and after iterative solution, the dynamic model formed by the displacement, the velocity and the acceleration with time can be obtained, namely: the variation curve of displacement, velocity, acceleration and time is shown in fig. 5.
Therefore, the bending moment and the axial force F can be obtainedz1And the time-varying curve of the equivalent stress thereof, from which the maximum equivalent stress can be obtained
And minimum equivalent force
See fig. 6. Thus stress ratio RσComprises the following steps:
in step S5, in consideration of the influence of the initial drill string defect, it is necessary to calculate the stress intensity factor and the geometry factor and determine the initial crack size by non-destructive inspection in the fatigue life calculation process. And determining the critical crack size according to the stress condition, and finally calculating the fatigue life according to the Walker model.
Therefore, step S5 specifically includes the following steps:
s51: the geometric form factor F of the bottom hole assembly is obtained by considering that most of the surface linear cracks are generated in the bottom hole assembly during the manufacturing and using processesm；
S52: obtaining a maximum stress intensity factor K of the bottom hole assembly from the geometric form factormax；
S53: measuring the initial crack size a of the bottom hole assembly0And obtaining the critical crack size a of the bottom hole assembly according to the fracture toughness of the material for preparing the bottom hole assembly and the stress condition of the bottom hole assemblyc；
S54: stress ratio and maximum stress intensity factor KmaxCritical crack size acThe fatigue life of the bottom hole assembly can be obtained by substituting the model into the Walker model.
Wherein the geometry factor F of the bottom hole assembly in S51mThe calculation formula of (A) is as follows:
Fm＝1+0.128(aL/Dp)-0.288(aL/Dp)2+1.525(aL/Dp)3 (56)；
in the formula, is a crack FmA shape factor; a isLM is half crack length; dpIs the drill string diameter.
Wherein the maximum stress intensity factor K in S52maxThe calculation formula of (A) is as follows:
wherein a is the crack depth, m.
Wherein the critical crack size a of the bottom hole assembly in S53cThe calculation formula of (A) is as follows:
in the formula, KICIs the fracture toughness of the material, MPa.m1/2。
Wherein, the Walker model in S54 is:
n is the stress cycle times and weeks; rσIs the stress ratio; c. n and m are material constants.
The fatigue life of the bottom hole assembly is the drill string depth from initial crack a0Propagation to critical crack depth acCycle of (d), and therefore, the calculation is:
the fatigue life of the bottom hole assembly under the load condition can be accurately simulated according to the obtained dynamic model, the stress model and the fatigue life calculation formula.
The ZS-25000 drill rod is taken as an example, and the basic parameters of the drill rod are shown in the table 1:
TABLE 1
Through a fatigue failure test of simulating the drill rod in a working state, composite load, torque, tension pressure, transverse bending moment and rotating speed are applied to the drill rod in the test, and load is addedThe loading mode adopts constant-amplitude loading, and each rotation in the test is 2 x 104And performing one-time destructive inspection on the drill rod to obtain drill rod fatigue life test data shown in a table 2, and predicting the fatigue life of the drill rod according to the prediction method provided by the application, wherein the prediction result is shown in the table 2.
TABLE 2
As can be seen from the table 2, the error between the experimental simulated fatigue life of the drill rod and the fatigue life predicted by the prediction method is less than 1%, the accuracy is high, the method has a more accurate simulated prediction effect on the drill rods at different rotating speeds, and the fatigue life prediction method is favorable for predicting the fatigue life of the drill rod running under different loads.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (10)
1. The method for predicting the fatigue life of the bottom hole assembly based on drill string dynamics is characterized by comprising the following steps of:
s1: dividing a bottom hole assembly of a target well into a plurality of units along a borehole axis, establishing coordinate axes by taking the borehole axis direction of the target well as a Z axis, a righteast direction as an X axis and a rightsouth direction as a Y axis, and obtaining the displacement vector form of the bottom hole assembly of each unit;
s2: obtaining a drill string dynamics model of the bottom hole assembly according to a Lagrange equation;
s3: assuming that the target well wall is rigid and the drilling assembly and the target well wall are in random contact, the force applied by the well wall when the bottom drilling assembly is in contact with the well wall comprises: obtaining a stress model when the drilling tool assembly is in contact with the well wall by axial friction resistance Fez, tangential friction resistance Fer, well wall torque Te and bending moment Me;
s4: setting the bottom hole assembly and boundary conditions, substituting a displacement vector equation of the bottom hole assembly into the drill string dynamic model, discretely solving the drill string dynamic model of each unit by adopting a generalized-alpha method, and obtaining the equivalent stress of the bottom hole assembly according to the stress model;
s5: setting initial conditions of the bottom hole assembly, obtaining the fatigue life of the bottom hole assembly according to the Walker model and the equivalent stress of the bottom hole assembly, in the fatigue life calculation process, firstly calculating a stress intensity factor and a geometric form factor, determining the initial crack size through nondestructive inspection, then determining the critical crack size according to the stress conditions, and finally calculating the fatigue life according to the Walker model.
2. The method of claim 1, wherein the bottomhole assembly generalized displacement vector equation for each of the units is:
U＝(Ux1 Uy1 Uz1 θx1 θy1 θz1 Ux2 Uy2 Uz2 θx2 θy2 θz2)T；
wherein, Ux1、Uy1、Uz1、Ux2、Uy2、Uz2Respectively linear displacement of each unit in each direction of two nodes; thetax1、θy1、θz1、θx2、θy2、θz2Respectively, the angular displacement of each unit in two nodes.
3. The method of claim 1, wherein the drill string dynamics model of the bottom hole assembly is:
wherein,
{ U }, { F } are generalized acceleration, generalized velocity, generalized displacement and generalized external force vector, respectively; [ M ] A]，[C]，[K]Respectively a mass matrix, a damping matrix and a stiffness matrix.
4. The method of claim 3, wherein the generalized external force vector comprises centrifugal and gravitational forces experienced at two nodes of each of the elements.
5. The method of claim 1, wherein the force model of the bottomhole assembly in contact with the borehole wall is:
wherein, FezIs axial frictional resistance, FerIs tangential frictional resistance, TeFor borehole wall torque, MeIs a bending moment; mu.seThe friction coefficient of the bottom drilling tool assembly and the well wall; diIs the wellbore diameter, m; fNIs the contact force, N.
6. The method of claim 1, wherein the bottomhole assembly boundary conditions comprise an upper boundary condition and a lower boundary condition, wherein the upper boundary condition is a force condition of the bottomhole assembly at the wellhead of the target well, and specifically comprises:
Ux＝0，UY＝0，UZ＝0，θz＝Ωt，θx＝0，θy＝0；
wherein, Ux、Uy、UzRespectively the displacement of the bottom drilling tool assembly at the wellhead; thetax、θy、θzRespectively the rotation angles of the bottom drilling tool assembly at the wellhead around each coordinate axis; omega is the rotating speed of the bottom drilling tool assembly, rad/s; t represents time, s;
the lower boundary condition is the stress condition of the bottom hole assembly at the wellhead of the target well; the method comprises the following steps:
wherein P represents an excitation force generated by the interaction of the drill bit with the formation; p0The amplitude of the exciting force is a constant given by well site data, KN; dbRepresents the bit diameter, m; n represents the rotating speed of the rotating disc; h represents the depth of cut, m, of one rotation of the drill bit; mu.sbRepresenting the coefficient of friction of the drill bit with the bottom of the well; t represents time, s; pwobRepresents the bottom hole weight on bit, KN; ω represents the rotational angular velocity of the drill, rad/s; WOB represents the combined force at the bottom of the well, KN; t ispRepresenting the torque, N · m, on the bottom hole assembly due to the interaction of the bit with the bottom hole.
7. The method of claim 1, wherein the prediction equation for the fatigue life of the bottom hole assembly is:
wherein, acCritical crack size, m; a is0Initial crack size, m; n is the stress cycle times and weeks; rσTo be in due courseForce ratio; sigmamaxThe maximum equivalent stress c, n and m are material constants; geometric form factor Fm。
8. The method of claim 1, wherein the drill string dynamics-based bottom hole assembly fatigue life prediction method is characterized in that in step S4, the drill string dynamics model is discretely solved by a generalized-alpha method.
9. The method of claim 8, wherein the drill string dynamics model solution specifically comprises the steps of:
s41: obtaining a general calculation formula of the generalized-alpha method according to the basic form of the generalized-alpha method;
s42: establishing a null matrix of a stiffness matrix [ K ], a mass matrix [ M ] and a damping matrix [ C ] and substituting the null matrix into a general calculation formula of a generalized-alpha method;
s43: assignment d0And v0And a obtained according to the basic form of the generalized-alpha method0A value;
s44: setting a time step length and a limit spectrum radius, and calculating a required integral constant;
s45: calculating to obtain an effective stiffness matrix, an effective load vector, displacement at the moment t + delta t, acceleration at the moment t + delta t and speed at the moment t + delta t;
s46: and (5) bringing the values obtained in the step (S45) into the drill string dynamic model, and performing iterative calculation to obtain time functions of model displacement, speed and acceleration.
10. The method of any of claims 1-9, wherein the prediction method is further based on the following assumptions:
the well bore is circular, the axis of the well bore is coincident with the axis of the bottom hole assembly under the initial condition, and no annular gap exists between the drill bit and the well wall;
the bottom hole assembly deforms to negligible micro deformation without considering the shear stress;
the effects of the bottom hole assembly sub and the threaded bore slots are not considered.
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