Fatigue life prediction method based on dynamic stress of drill string

Abstract

The invention belongs to the field of petroleum and natural gas development, and particularly relates to a fatigue life prediction method based on drill string dynamic stress, and the method comprises the following steps: inputting basic parameters: the basic parameters comprise a well track, a bottom drilling tool combination, a drill string structure and drilling parameters; according to a Lagrange equation, a drill string system dynamic model is established; node velocity, displacement and acceleration are obtained through a drill string system dynamics model, and drill string dynamic equivalent stress is calculated according to the node velocity, displacement and acceleration; counting a stress amplitude and a stress mean value by adopting a rain flow counting method; correcting the stress amplitude and the stress mean value by adopting a goodman formula; substituting into an S-N curve and calculating to obtain the fatigue life. According to the method, the fatigue life of the whole-well drill string can be analyzed, the fatigue service life of the whole-well drill string under the working condition is predicted through data analysis and processing, the presented result is the specific service time of the drill string, and the method has a very strong guiding effect on field engineering practice.

Description

Technical Field

[0001] This application belongs to the field of oil and gas development, and specifically relates to a fatigue life prediction method based on drill string dynamic stress. Background Technology

[0002] During ultra-deep well drilling, the downhole drill string will be subjected to more complex loads, including tensile, compressive, torsional, bending, impact, and hydrostatic pressure, with the number, location, and induction time of these loads constantly changing. Furthermore, the load and stress variations in complex well structures are greater and more complex, leading to reduced fatigue strength and a significantly increased probability of failure. Drill string wear, fracture, leakage, and deformation not only significantly increase drilling costs but also extend tripping times, severely hindering normal drilling operations and reducing the rate of penetration (ROP). Therefore, a drill string fatigue life prediction method is needed to quantify drill string lifespan and provide guidance for drill string use and maintenance.

[0003] Statistics show that among all causes of drill string failure, fatigue accounts for 68%, drill string overload accounts for 17%, drill string corrosion accounts for 4%, and failures caused by other reasons account for only 1%. Therefore, drill string fatigue and overload are the main causes of its failure, and drill string vibration is the most important factor causing drill string fatigue and overload. Previously, many scholars analyzed drill string vibration, including lateral vibration, axial vibration, and torsional vibration, but these studies were mostly qualitative and could not provide quantitative guidance for drill string use. Based on this, a few scholars have proposed related drill string fatigue research. In 2020, Yang Chunxu of China University of Petroleum established a dynamic stress calculation model for bottom drill string assembly considering the contact collision between the drill string and the wellbore and dynamic excitation, using a safety factor to characterize the drill string's safety performance. Also in 2020, Yin Mao of Nantong University used finite element software to conduct numerical simulation and fatigue life prediction analysis on drill pipe models with cracks containing different geometric parameters. This method qualitatively judges the fatigue condition by using the number of cycles. In 2021, Wu Yuandeng of Yangtze University established a finite element model for calculating the fatigue life of coiled tubing during drilling and milling bridge plug operations using ABAQUS software. He calculated the fatigue life of the coiled tubing under combined internal pressure and torque loads. This fatigue method is similar to the evaluation method proposed by Yin Mao of Nantong University. In 2022, Mao Liangjie of Southwest Petroleum University published a paper titled "Research on Fatigue Life of Bottom Drill String Assembly Based on Drill String Dynamics." The paper proposed using drill string dynamics calculation results to study the fatigue life of the drill string. However, the fatigue calculation results were only in cycles, which had little practical significance for field use and could not quantify the service life of the drill string. In 2024, Wang Wenchang of Shanghai University published a paper titled "Dynamic Fatigue Failure Characteristics and Parameter Optimization of Ultra-Deep Well Drill Strings." The author, also based on the dynamic characteristics of the entire well drill string and fatigue damage theory, proposed a fatigue safety factor. Although the author had a fatigue safety judgment standard, it could only qualitatively assess the magnitude of the drill string fatigue failure risk and could not quantitatively analyze the fatigue life and service time of the drill string, thus having low reference value for field use. In addition, some scholars have been granted related invention patents in recent years. In 2020, Ma Xiaocheng of PetroChina was granted an invention patent entitled "Analysis Method of Fatigue Life of Horizontal Directional Drill Pipe", and in 2022, Mao Liangjie of Southwest Petroleum University was granted an invention patent entitled "Research on Fatigue Life of Bottom Drill String Assembly Based on Drill String Dynamics". The above invention patents also have similar problems to previous studies. They all use cycles to characterize the fatigue life of the drill string. However, since the cycles are not timed, they cannot provide an effective reference for the use and maintenance of the drill string in the field.

[0004] The survey found that existing fatigue life prediction methods are mostly theoretical analyses, which cannot quantitatively assess the specific service life of drill strings and are difficult to provide effective references for the field.

[0005] Existing patents, such as Chinese invention patent application CN113065211A entitled "A Method for Predicting the Fatigue Life of Bottom Drill String Assemblies Based on Drill String Dynamics," disclose the following: This invention discloses a method for predicting the fatigue life of bottom drill string assemblies based on drill string dynamics, relating to the field of oil and gas development technology, including the following steps: S1: Establishing coordinate axes and obtaining the displacement vector form of the bottom drill string assembly for each unit; S2: Obtaining the drill string dynamics model according to the Lagrange equation; S3: Obtaining the force model of the drill string assembly when in contact with the wellbore; S4: Discretely solving the drill string dynamics model of each unit and obtaining the equivalent stress of the bottom drill string assembly based on the force model; S5: Obtaining the fatigue life of the bottom drill string assembly. The above patent mainly focuses on bottom drill string assemblies, proposing a fatigue life analysis method for bottom drill string assemblies. Its main drawback is: 1. It mainly analyzes the fatigue life of bottom drill string assemblies, but in areas with large doglegs such as the build-up section, the drill string also experiences alternating stress, which may also lead to fatigue failure. 2. The result presented is the number of alternating stresses that occurred in the drill string within a calculation time. It calculates the number of alternating stresses in the drill string, rather than the fatigue life of the drill string. In essence, it does not have the function of predicting the fatigue life of the drill string, which is of little practical guiding value to the engineering site. Summary of the Invention

[0006] To address the technical challenge of drill string fatigue failure caused by vibration during drilling, a fatigue life prediction method based on drill string dynamic stress is proposed. This method can predict the specific service life of the drill string and quantify its fatigue loss.

[0007] To achieve the above-mentioned technical effects, the technical solution of this application is as follows:

[0008] A fatigue life prediction method based on drill string dynamic stress includes the following steps:

[0009] Step S1. Input basic parameters: Basic parameters include wellbore trajectory, bottom hole assembly, drill string structure, and drilling parameters;

[0010] Step S2. Establish a dynamic model of the drill string system based on the Lagrange equations;

[0011] Step S3. Obtain the node velocity, displacement, and acceleration using the drill string system dynamic model from Step S2, and calculate the dynamic equivalent stress of the drill string accordingly;

[0012] Step S4. Use the rainflow counting method to count the stress amplitude and mean stress.

[0013] Step S5. Correct the stress amplitude and mean stress using the Goodman formula;

[0014] Step S6. Substitute the SN curve to calculate the fatigue life.

[0015] Furthermore, the specific content of step S2 includes:

[0016] A two-node beam element is used to discretize the continuous drill string in a complex wellbore structure. Each node has 6 degrees of freedom, including 3 translational (x, y, z) and 2 lateral rotation angles (θ). y ,θ z ) and a twist angle θ x ,like Figure 1 As shown, i and j represent the nodes above and below the beam element. The drill string motion can be represented by the displacement vectors of the beam element nodes:

[0017] {U i} e =[x i ,y i ,z i ,θ xi ,θ yi ,θ zi ,x j ,y j ,z j ,θ xj ,θ yj ,θ zj (1)

[0018] The relationship between the kinetic energy, potential energy, and work done by external forces in a drill string system can be expressed as: Hamilton's principle

[0019]

[0020] In the formula, T is the kinetic energy of the drill string system; V is the potential energy of the drill string system; W is the work done by external forces on the drill string system; δ represents the variational operation, which refers to a small change in a certain quantity; Δt represents a certain time interval.

[0021] Using the finite element method, the drill string system is discretized into multiple continuous Euler-Bernoulli beam elements with two nodes each. The discretized beam elements are then rewritten as the Lagrange equations governing the drill string motion.

[0022]

[0023] In the formula, U i F represents the nodal displacement. i External forces at the nodes.

[0024] Furthermore, substituting the translational kinetic energy, rotational kinetic energy, potential energy, gravity, and centrifugal force of the beam element into equation (3), we obtain the control equation for the drill string dynamics, which can be written in matrix form as follows:

[0025]

[0026] In the formula, {U} and {F} are the generalized acceleration, velocity, displacement, and external force vectors, respectively. [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix.

[0027] Furthermore, the boundary conditions of the drill string system include: the upper end of the drill string is subjected to the tension of the drill string below and the torque provided by the rotary table; the lower end of the drill string is subjected to the axial excitation and resistance torque generated by the interaction between the drill bit and the rock; and the positive contact force, tangential friction force and friction torque of the wellbore on the drill string.

[0028] Furthermore,

[0029] The total kinetic energy of a beam element includes the translational kinetic energy and the rotational kinetic energy of the beam element, and its expression is:

[0030]

[0031] In the formula, ρ represents the translational velocity along the X, Y, and Z axes, in m / s; ρ is the density of the drill string, in kg / m³. 3 A is the cross-sectional area of ​​the beam element, in meters. 2 ;e represents the cross-sectional eccentricity, in meters; Ω refers to the actual rotational speed of the downhole drill string, in rad / s; l e I is the length of the beam element, in meters. x It is the polar moment of inertia of the beam element section, m 4 ;I yz It is the moment of inertia of the cross section of the beam element, m 4 ;

[0032] The potential energy expression for a beam element is:

[0033]

[0034] In the formula, u x It is the displacement in the x-axis direction, θ x θ represents the angle of twist about the x-axis. y θ z Indicates the rotation angles about the y-axis and z-axis, , respectively, are the translational velocities on the X, Y, and Z axes; E is the elastic modulus of the drill string, Pa; G is the shear modulus of the drill string, Pa; the first four terms in equation (5) are linear stiffness matrices, the fifth and sixth terms are nonlinear stiffness matrices of the coupled axial deformation and bending deformation of the drill string, and the last two terms represent nonlinear stiffness matrices of the coupled torsional deformation and bending deformation of the drill string.

[0035] The components of gravity of the beam element in x, y, and z can be expressed as:

[0036]

[0037] In the formula, q represents the equivalent gravity of a 1m drill string, N / m; α is the angle between the beam element axis and the vertical direction; therefore, the equivalent nodal force of the gravity vector is:

[0038]

[0039] In the formula, L represents the length of the drill string element, in meters (m). The cross-section of the drill string is not a centrally symmetric model, therefore centrifugal force exists during rotation. The centrifugal forces between the two elements in the x, y, and z directions are:

[0040]

[0041] In the formula, β is the phase angle of the centroid, in rad; for the centrifugal force vector of the node, its equivalent force can be expressed as:

[0042]

[0043] Furthermore, the specific content of step S3 includes:

[0044] Displacement, velocity, acceleration, and external force vectors are the results of iterative solutions to the drill string dynamics control equations and are stored in [the database / system]. In the four matrices {U} and {F};

[0045] Normal stress σ acting on the drill string x The shear stress τ is expressed as:

[0046]

[0047] In the formula, F x A represents the dynamic axial force borne by the drill string node, expressed in N (N). x M represents the cross-sectional area of ​​a drill string element, in meters (m). y M is the bending moment of the drill string at the y-axis section. z Let d be the bending moment of the drill string at the z-axis section. o d is the outer diameter of the drill string, in meters (m). i T0 is the inner diameter of the drill string, in meters (m); T0 is the torque acting on the drill string, in Nm; I y It is the moment of inertia along the y-axis, I z It is the moment of inertia along the z-axis.

[0048] Furthermore, based on the Mohr stress circle criterion, the first principal stress σ1, the second principal stress σ2, and the third principal stress σ3 of the drill string are calculated.

[0049]

[0050] The equivalent stress expression at a certain location and time in the drill string is written as:

[0051]

[0052] Furthermore, the specific content of step S4 includes:

[0053] The continuous load-time history is discretized into a series of peaks and valleys using the rainflow counting method. The random load spectrum is obtained by performing cyclic counting statistical processing, and the mean stress and stress amplitude at each position of the drill string are obtained.

[0054] Furthermore, the content of step S5 is as follows:

[0055] The general expression for the Goodman curve is:

[0056]

[0057] In the formula, S a S represents the stress amplitude. e For the fatigue limit, S m The mean stress, σ b For tensile strength and fatigue limit S e and tensile strength σ b It is determined by the properties of the material itself.

[0058] The equivalent mean of amplitude-mean-order under the Goodman curve is obtained by using the rainflow method, i.e., the stress amplitude S when the mean is 0. i :

[0059]

[0060] In the formula, S i S is the converted zero-mean stress amplitude. ai For the i-th stress amplitude, S mi Let σ be the mean stress value of the i-th stress. b Tensile strength.

[0061] Furthermore, step S6 includes:

[0062] The SN curve is obtained through fatigue experiments, where S represents the stress amplitude and N represents the number of cycles.

[0063] S = 2513.6 N -0 .132 (16)

[0064] N = S -7.576 *2513.6 7.576 (17)

[0065] Finally, the corrected zero-mean stress amplitude is substituted into the SN curve, and the fatigue life is solved using Miner's linear cumulative damage theory. Finally, combined with the calculation time, the service life of the drill string can be directly obtained.

[0066] Furthermore, in Miner's theory, when a material is subjected to stress cycles of different amplitudes, each stress amplitude will cause damage to the material's fatigue life. The total fatigue damage of the material is predicted by accumulating these damages; each stress amplitude S i The damage Di resulting from the corresponding number of cycles Ni is defined as:

[0067]

[0068] Where ni is the actual number of cycles the material undergoes under stress amplitude Si;

[0069] The total damage D of the material is calculated using the following formula:

[0070]

[0071] When D = 1, the material reaches the critical state of failure or damage; when D < 1, the material has not yet reached fatigue failure.

[0072] The service life P of the drill string is calculated using the following formula:

[0073] P = D × t (20)

[0074] In the formula, P is the service life of the drill string, and t is the calculation time.

[0075] This application has the following technical effects:

[0076] Fatigue damage caused by drill string vibration during drilling processes, both domestically and internationally, significantly impacts drilling safety, necessitating an efficient matching method to address this challenge. This application proposes a novel fatigue life prediction method based on drill string dynamic stress. It utilizes a drill string dynamics model to calculate the dynamic equivalent stress of the drill string at various locations throughout the well during actual drilling. Then, the rainflow counting method is used to statistically obtain the stress amplitude and mean stress at each location. The Goodman formula is then applied to correct these stress amplitude and mean stress values, ultimately calculating the fatigue life of the drill string. This achieves a quantitative assessment of drill string fatigue life.

[0077] This application can analyze the fatigue life of the entire well drill string. Through data analysis and processing, this application predicts the fatigue service life of the entire well drill string under this working condition. The result presented is the specific service time of the drill string, which has a strong guiding role in actual field engineering.

[0078] The drill string dynamics model proposed in step S2 is a highly accurate Euler beam element drill string dynamics model. The safety analysis model proposed in step S3 also falls under the category of structural mechanics. By linking the two models, the dynamic stress of the drill string (i.e., the time history curve of stress variation) is output. Previously, drill string stress was often calculated by neglecting time, assuming the stress at all locations throughout the well to be a constant value before calculating fatigue life. However, the drill string rotates continuously downhole, and the stress is not constant. The dynamic stress of the drill string obtained using the drill string dynamics model in this application can better reflect the dynamic changes in the stress on the drill string.

[0079] Step S5 proposes the Goodman curve formula. The applicant has optimized the formula using fatigue test data in order to adapt to the fatigue characteristics of the drill string.

[0080] In step S6, the SN curve is obtained by coupling fatigue test data. Equations (16) and (17) are improvements based on previous work. Since this formula is optimized by fitting data from drill string fatigue tests, it can better describe the fatigue process of the drill string.

[0081] This application utilizes a drill string dynamics model to solve for the drill string's dynamic characteristics; it then uses this data to solve for the drill string's dynamic stress curve; next, it processes the dynamic stress data using the rainflow counting method and corrects it with a Goodman curve; finally, it substitutes the data into the SN curve to obtain fatigue loss and converts it into service life. This method is the first of its kind proposed in the field of oil and gas well string mechanics. Although existing technologies have also proposed fatigue assessment methods, their assessment standards are based on fatigue cycles or fatigue safety factors, which are qualitative analyses and cannot provide quantitative opinions for the use and maintenance of drill strings in the field. Based on this, this application quantitatively describes the specific service life of the drill string. Attached Figure Description

[0082] Figure 1 This is the whole-well drill string dynamics model of the present invention.

[0083] Figure 2 The Goodman curve calculated for this invention.

[0084] Figure 3 This is the SN data obtained by fatigue experiments in this invention.

[0085] Figure 4 This is the SN curve obtained by fatigue testing in this invention.

[0086] Figure 5 This is the time history curve of equivalent stress at a certain location.

[0087] Figure 6 The stress amplitude at each location was obtained using the rainflow counting method.

[0088] Figure 7 The average stress at each location was obtained using the rainflow counting method.

[0089] Figure 8 This represents the zero-mean stress amplitude after correction using the Goodman formula. Detailed Implementation

[0090] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0091] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0092] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0093] In the description of this application, it should be noted that the terms "upper," "vertical," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use, or the orientation or positional relationship commonly understood by those skilled in the art. They are used only for the convenience of describing this application 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 on this application. In addition, the terms "first," "second," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0094] In the description of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "set," "install," and "connect" 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; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0095] Example 1

[0096] A fatigue life prediction method based on drill string dynamic stress includes the following steps:

[0097] Step S1. Input basic parameters: Basic parameters include wellbore trajectory, bottom hole assembly, drill string structure, and drilling parameters;

[0098] Step S2. Based on the Lagrange equations and considering the boundary conditions such as the kinetic energy, potential energy, work done by external forces, and wellbore constraints of the drill string, establish a dynamic model of the drill string system, such as... Figure 1 As shown;

[0099] Step S3. Obtain the node velocity, displacement, and acceleration using the drill string system dynamic model from Step S2, and calculate the dynamic equivalent stress of the drill string accordingly;

[0100] Step S4. Use the rainflow counting method to count the stress amplitude and mean stress.

[0101] Step S5. Correct the stress amplitude and mean stress using the Goodman formula;

[0102] Step S6. Substitute the SN curve to calculate the fatigue life.

[0103] Fatigue damage caused by drill string vibration during drilling processes, both domestically and internationally, significantly impacts drilling safety, necessitating an efficient matching method to address this challenge. This application proposes a novel fatigue life prediction method based on drill string dynamic stress. It utilizes a drill string dynamics model to calculate the dynamic equivalent stress of the drill string at various locations throughout the well during actual drilling. Then, the rainflow counting method is used to statistically obtain the stress amplitude and mean stress at each location. The Goodman formula is then applied to correct these stress amplitude and mean stress values, ultimately calculating the fatigue life of the drill string. This achieves a quantitative assessment of drill string fatigue life.

[0104] This application can analyze the fatigue life of the entire well drill string. Through data analysis and processing, this application predicts the fatigue service life of the entire well drill string under this working condition. The result presented is the specific service time of the drill string, which has a strong guiding role in actual field engineering.

[0105] Example 2

[0106] A fatigue life prediction method based on drill string dynamic stress includes the following steps:

[0107] Step S1. Input basic parameters: Basic parameters include wellbore trajectory, bottom hole assembly, drill string structure, and drilling parameters;

[0108] Step S2. Based on the Lagrange equations and considering the boundary conditions such as the kinetic energy, potential energy, work done by external forces, and wellbore constraints of the drill string, establish a dynamic model of the drill string system, such as... Figure 1 As shown;

[0109] Step S3. Obtain the node velocity, displacement, and acceleration using the drill string system dynamic model from Step S2, and calculate the dynamic equivalent stress of the drill string accordingly;

[0110] Step S4. Use the rainflow counting method to count the stress amplitude and mean stress.

[0111] Step S5. Correct the stress amplitude and mean stress using the Goodman formula;

[0112] Step S6. Substitute the SN curve to calculate the fatigue life.

[0113] The specific content of step S2 includes:

[0114] A two-node beam element is used to discretize the continuous drill string in a complex wellbore structure. Each node has 6 degrees of freedom, including 3 translational (x, y, z) and 2 lateral rotation angles (θ). y ,θ z ) and a twist angle θ x Let i and j represent the nodes above and below the beam element. The motion of the drill string is represented by the displacement vectors of the beam element nodes.

[0115] {U i} e =[x i ,y i ,z i ,θ xi ,θ yi ,θ zi ,x j ,y j ,z j ,θ xj ,θ yj ,θ zj (1)

[0116] The relationship between the kinetic energy, potential energy, and work done by external forces in a drill string system can be expressed as: Hamilton's principle

[0117]

[0118] In the formula, T is the kinetic energy of the drill string system; V is the potential energy of the drill string system; W is the work done by external forces on the drill string system; δ represents the variational operation, which refers to a small change in a certain quantity; Δt represents a certain time interval.

[0119] Using the finite element method, the drill string system is discretized into multiple continuous Euler-Bernoulli beam elements with two nodes each. The discretized beam elements are then rewritten as the Lagrange equations governing the drill string motion.

[0120]

[0121] In the formula, U i F represents the nodal displacement. i External forces at the nodes.

[0122] Substituting the translational kinetic energy, rotational kinetic energy, potential energy, gravity, and centrifugal force of the beam element into equation (3), we obtain the control equations for the drill string dynamics, which can be written in matrix form as follows:

[0123]

[0124] In the formula, {U} and {F} are the generalized acceleration, velocity, displacement, and external force vectors, respectively. [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix.

[0125] The boundary conditions of the drill string system include: the upper end of the drill string is hinged at the wellhead and subjected to the tension of the drill string below and the torque provided by the rotary table; the lower end of the drill string is at the drill bit and subjected to the axial excitation and resistance torque generated by the interaction between the drill bit and the rock; the constraint effect of the wellbore on the drill string is mainly subjected to the positive contact force, tangential friction force and friction torque.

[0126] The total kinetic energy of a beam element includes the translational kinetic energy and the rotational kinetic energy of the beam element, and its expression is:

[0127]

[0128] In the formula, ρ represents the translational velocity along the X, Y, and Z axes, in m / s; ρ is the density of the drill string, in kg / m³. 3 A is the cross-sectional area of ​​the beam element, in meters. 2 ;e represents the cross-sectional eccentricity, in meters; Ω refers to the actual rotational speed of the downhole drill string, in rad / s; l e I is the length of the beam element, in meters. x It is the polar moment of inertia of the beam element section, m 4 ;I yz It is the moment of inertia of the cross section of the beam element, m 4 ;

[0129] The potential energy expression for a beam element is:

[0130]

[0131] In the formula, u x It is the displacement in the x-axis direction, θ x θ represents the angle of twist about the x-axis. y θ z Indicates the rotation angles about the y-axis and z-axis, , respectively, are the translational velocities on the X, Y, and Z axes; E is the elastic modulus of the drill string, Pa; G is the shear modulus of the drill string, Pa; the first four terms in equation (5) are linear stiffness matrices, the fifth and sixth terms are nonlinear stiffness matrices of the coupled axial deformation and bending deformation of the drill string, and the last two terms represent nonlinear stiffness matrices of the coupled torsional deformation and bending deformation of the drill string.

[0132] The components of gravity of the beam element in x, y, and z can be expressed as:

[0133]

[0134] In the formula, q represents the equivalent gravity of a 1m drill string, N / m; α is the angle between the beam element axis and the vertical direction. Therefore, the equivalent nodal force of the gravity vector is:

[0135]

[0136] In the formula, L represents the length of the drill string element, in meters (m). The cross-section of the drill string is not a centrally symmetric model, therefore centrifugal force exists during rotation. The centrifugal forces between the two elements in the x, y, and z directions are:

[0137]

[0138] In the formula, β is the phase angle of the centroid, in rad; for the centrifugal force vector of the node, its equivalent force can be expressed as:

[0139]

[0140] The specific content of step S3 includes:

[0141] Displacement, velocity, acceleration, and external force vectors are the results of iterative solutions to the drill string dynamics control equations and are stored in [the database / system]. In the four matrices {U} and {F};

[0142] Normal stress σ acting on the drill string x The shear stress τ is expressed as:

[0143]

[0144] In the formula, F x A represents the dynamic axial force borne by the drill string node, expressed in N (N). x M represents the cross-sectional area of ​​a drill string element, in meters (m). y M is the bending moment of the drill string at the y-axis section. z Let d be the bending moment of the drill string at the z-axis section. o d is the outer diameter of the drill string, in meters (m). i T0 is the inner diameter of the drill string, in meters (m); T0 is the torque acting on the drill string, in Nm; I yIt is the moment of inertia along the y-axis, I z It is the moment of inertia along the z-axis.

[0145] Based on the Mohr stress circle criterion, the first principal stress σ1, the second principal stress σ2, and the third principal stress σ3 of the drill string are calculated.

[0146]

[0147] If the drill string satisfies the fourth strength theory under small deformation, then the equivalent stress expression at a certain position and time of the drill string can be written as:

[0148]

[0149] The specific content of step S4 includes:

[0150] Since the equivalent stress of the drill string calculated using the whole-well drill string dynamics model is an asymmetric random load, and the SN curve represents the material fatigue life under a stress ratio of -1 and a mean stress of 0, it cannot be directly used to calculate the drill string fatigue life. Therefore, the rainflow counting method is used to discretize the continuous load-time history into a series of peaks and valleys, and perform cyclic counting statistical processing to obtain the random load spectrum, thereby obtaining the mean stress and stress amplitude at each location of the whole-well drill string.

[0151] Rainflow counting requires rotating the strain-time history data to the horizontal plane of the stress amplitude coordinate axis. The data is like individual roofs, with rainwater flowing down them. Figure 6 and Figure 7 As shown, the basic counting rules of the rainflow counting method are as follows:

[0152] (1) Rain flowed down the slope from the peak (valley) position of the load-time data;

[0153] (2) When a rain stream starts flowing at a certain peak point, it stops flowing when it encounters a larger peak point; when a rain stream starts flowing at a certain valley point, it stops flowing when it encounters a smaller valley point.

[0154] (3) If the rainwater flow encounters the rainwater flow from the roof above, it must stop flowing and form a cycle;

[0155] (4) Draw each cycle according to the start and end points of the raindrop flow, extract all cycles one by one, and record their peak and valley values.

[0156] (5) The horizontal length of each rain stream is taken as the amplitude of the cycle.

[0157] In the rainflow method, each part of the load-time data recording process is included and counted only once. The truncation of a small cycle at a significant load amplitude does not affect the damage it causes, and the truncated small cycles are superimposed on larger cycles. Therefore, the fatigue life of the component can be estimated based on cumulative damage theory, yielding relatively good results. Given that the rainflow method considers the mean and amplitude of the load, the plastic deformation of the structure, and has a certain mechanical basis, it also possesses advantages such as the ability to quickly and accurately perform cycle counting through computer programming.

[0158] The content of step S5 is as follows:

[0159] like Figure 2 As shown, the general expression for the Goodman curve is:

[0160]

[0161] In the formula, S a S represents the stress amplitude. e For the fatigue limit, S m The mean stress, σ b For tensile strength and fatigue limit S e and tensile strength σ b Determined by the inherent properties of the material, S in this embodiment e =300MPa, σ b =1222MPa.

[0162] The equivalent mean of amplitude-mean-order under the Goodman curve is obtained by using the rainflow method, i.e., the stress amplitude S when the mean is 0. i :

[0163]

[0164] In the formula, S i S is the converted zero-mean stress amplitude. ai For the i-th stress amplitude, S mi Let σ be the mean stress value of the i-th stress. b Tensile strength.

[0165] Substituting the stress amplitude and mean stress into equation (15), the calculated S i This is the corrected stress amplitude, and the corrected stress mean is 0.

[0166] Step S6 includes:

[0167] like Figure 3 , Figure 4 As shown, the SN curve is obtained through fatigue testing. The SN curve is obtained by experimental measurement using a sample of specified size, where S represents the stress amplitude and N represents the number of cycles.

[0168] S = 2513.6 N -0.132 (16)

[0169] N = S -7.576 *2513.6 7.576 (17)

[0170] Finally, the corrected zero-mean stress amplitude is substituted into the SN curve, and the fatigue life is solved using Miner's linear cumulative damage theory. Finally, combined with the calculation time, the service life of the drill string can be directly obtained.

[0171] Furthermore, in Miner's theory, when a material is subjected to stress cycles of different amplitudes, each stress amplitude will cause damage to the material's fatigue life. The total fatigue damage of the material is predicted by accumulating these damages; each stress amplitude S i The damage Di resulting from the corresponding number of cycles Ni (i.e., the fatigue life at that stress amplitude) is defined as:

[0172]

[0173] Where ni is the actual number of cycles the material undergoes under stress amplitude Si;

[0174] The total damage D of the material is calculated using the following formula:

[0175]

[0176] According to Miner's theory, when D = 1, the material reaches the critical state of failure or damage; when D < 1, the material has not yet reached fatigue failure.

[0177] The service life P of the drill string is calculated using the following formula:

[0178] P = D × t (20)

[0179] In the formula, P is the service life of the drill string, and t is the calculation time.

[0180] Fatigue damage caused by drill string vibration during drilling processes, both domestically and internationally, significantly impacts drilling safety, necessitating an efficient matching method to address this challenge. This application proposes a novel fatigue life prediction method based on drill string dynamic stress. It utilizes a drill string dynamics model to calculate the dynamic equivalent stress of the drill string at various locations throughout the well during actual drilling. Then, the rainflow counting method is used to statistically obtain the stress amplitude and mean stress at each location. The Goodman formula is then applied to correct these stress amplitude and mean stress values, ultimately calculating the fatigue life of the drill string. This achieves a quantitative assessment of drill string fatigue life.

[0181] This application can analyze the fatigue life of the entire well drill string. Through data analysis and processing, this application predicts the fatigue service life of the entire well drill string under this working condition. The result presented is the specific service time of the drill string, which has a strong guiding role in actual field engineering.

[0182] The drill string dynamics model proposed in step S2 is a highly accurate Euler beam element drill string dynamics model. The safety analysis model proposed in step S3 also falls under the category of structural mechanics. By linking the two models, the dynamic stress of the drill string (i.e., the time history curve of stress variation) is output. Previously, drill string stress was often calculated by neglecting time, assuming the stress at all locations throughout the well to be a constant value before calculating fatigue life. However, the drill string rotates continuously downhole, and the stress is not constant. The dynamic stress of the drill string obtained using the drill string dynamics model in this application can better reflect the dynamic changes in the stress on the drill string.

[0183] Step S5 proposes the Goodman curve formula. The applicant has optimized the formula using fatigue test data in order to adapt to the fatigue characteristics of the drill string.

[0184] In step S6, the SN curve is obtained by coupling fatigue test data. Equations (6) and (17) are improvements based on previous work. Since this formula is optimized by fitting data from drill string fatigue tests, it can better describe the fatigue process of the drill string.

[0185] This application utilizes a drill string dynamics model to solve for the drill string's dynamic characteristics; it then uses this data to solve for the drill string's dynamic stress curve; next, it processes the dynamic stress data using the rainflow counting method and corrects it with a Goodman curve; finally, it substitutes the data into the SN curve to obtain fatigue loss and converts it into service life. This method is the first of its kind proposed in the field of oil and gas well string mechanics. Although existing technologies have also proposed fatigue assessment methods, their assessment standards are based on fatigue cycles or fatigue safety factors, which are qualitative analyses and cannot provide quantitative opinions for the use and maintenance of drill strings in the field. Based on this, this application quantitatively describes the specific service life of the drill string.

[0186] Example 3

[0187] The calculation process for the fatigue life of the entire well drill string is as follows:

[0188] S2 and S3 use the dynamic model of the whole well drill string system to solve for the dynamic equivalent stress of the drill string at each position in the whole well (5).

[0189] S4 then used the rainflow counting method to statistically obtain the stress amplitude at each location. Figure 6 ) and mean stress ( Figure 7 ).

[0190] S5 uses the Goodman formula to correct the stress amplitude and mean stress. Figure 8 ).

[0191] S6 then substitutes the zero-mean stress amplitude into the SN curve to calculate the fatigue life, and converts it into fatigue loss based on the number of cycles under different stresses. The fatigue loss at this time is the fatigue loss of the drill string within the simulation time (for example, if the simulation time is 5s and the fatigue loss is 0.0000001, it means that the drill string fatigue loss is 0.0000001 every 5s). Assuming that the drill string is unusable after the fatigue loss reaches 0.5, the usable lifespan is 0.5 / 0.0000001*5s / 3600=1388.889h.

[0192] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0193] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A fatigue life prediction method based on drill string dynamic stress, characterized in that, Includes the following steps: Step S1. Input basic parameters: Basic parameters include wellbore trajectory, bottom hole assembly, drill string structure, and drilling parameters; Step S2. Establish a dynamic model of the drill string system based on the Lagrange equations; Step S3. Obtain the node velocity, displacement, and acceleration using the drill string system dynamic model from Step S2, and calculate the dynamic equivalent stress of the drill string accordingly; Step S4. Use the rainflow counting method to count the stress amplitude and mean stress. Step S5. Correct the stress amplitude and mean stress using the Goodman formula; Step S6. Substitute the SN curve to calculate the fatigue life.

2. The fatigue life prediction method based on drill string dynamic stress according to claim 1, characterized in that, The specific content of step S2 is as follows: A two-node beam element is used to discretize the continuous drill string in a complex wellbore structure. Each node has 6 degrees of freedom, including 3 translational (x, y, z) and 2 lateral rotation angles (θ). y ,θ z ) and a twist angle θ x Let i and j represent the nodes above and below the beam element. The motion of the drill string is represented by the displacement vectors of the beam element nodes. {U i } e =[x i ,y i ,z i ,i xi ,i yi ,i zi ,x j ,y j ,z j ,i xj ,i yj ,i zj ] (1) The relationship between the kinetic energy, potential energy, and work done by external forces in a drill string system can be expressed as: Hamilton's principle In the formula, T is the kinetic energy of the drill string system; V is the potential energy of the drill string system; W is the work done by external forces on the drill string system; δ represents the variational operation, which refers to a small change in a certain quantity; Δt represents a certain time interval.

3. The fatigue life prediction method based on drill string dynamic stress according to claim 2, characterized in that, Using the finite element method, the drill string system is discretized into multiple continuous Euler-Bernoulli beam elements with two nodes each. The discretized beam elements are then rewritten as the Lagrange equations governing the drill string motion. In the formula, U i F represents the nodal displacement. i External forces at the nodes.

4. The fatigue life prediction method based on drill string dynamic stress according to claim 3, characterized in that, Substituting the translational kinetic energy, rotational kinetic energy, potential energy, gravity, and centrifugal force of the beam element into equation (3), we obtain the control equations for the drill string dynamics, which can be written in matrix form as follows: In the formula, {U} and {F} are the generalized acceleration, velocity, displacement, and external force vectors, respectively. [M] is the mass matrix, [C] is the damping matrix, and [K] is the stiffness matrix.

5. The fatigue life prediction method based on drill string dynamic stress according to claim 3, characterized in that, The boundary conditions of the drill string system include: the upper end of the drill string is subjected to the tension of the drill string below and the torque provided by the rotary table; the lower end of the drill string is subjected to the axial excitation and resistance torque generated by the interaction between the drill bit and the rock; and the positive contact force, tangential friction force and friction torque of the wellbore on the drill string.

6. The fatigue life prediction method based on drill string dynamic stress according to claim 4, characterized in that, The total kinetic energy of a beam element includes the translational kinetic energy and the rotational kinetic energy of the beam element, and its expression is: In the formula, ρ represents the translational velocity along the X, Y, and Z axes, in m / s; ρ is the density of the drill string, in kg / m³. 3 A is the cross-sectional area of ​​the beam element, m. 2 ; e represents the cross-sectional eccentricity, m; ... refers to the actual rotational speed of the downhole drill string, rad / s; l e It is the length of the beam element, in meters (m). I x It is the polar moment of inertia of the beam element section, m 4 ; I yz It is the moment of inertia of the cross section of the beam element, m 4 ; The potential energy expression for a beam element is: In the formula, u x It is the displacement in the x-axis direction, θ x θ represents the angle of twist about the x-axis. y θ z Indicates the rotation angles about the y-axis and z-axis, , respectively, are the translational velocities on the X, Y, and Z axes; E is the elastic modulus of the drill string, Pa; G is the shear modulus of the drill string, Pa; the first four terms in equation (5) are linear stiffness matrices, the fifth and sixth terms are nonlinear stiffness matrices of the coupled axial deformation and bending deformation of the drill string, and the last two terms represent nonlinear stiffness matrices of the coupled torsional deformation and bending deformation of the drill string. The components of gravity of the beam element in x, y, and z can be expressed as: In the formula, q represents the equivalent gravity of a 1m drill string, N / m; α is the angle between the beam element axis and the vertical direction; therefore, the equivalent nodal force of the gravity vector is: In the formula, L represents the length of the drill string element, in meters (m). The cross-section of the drill string is not a centrally symmetric model, therefore centrifugal force exists during rotation. The centrifugal forces between the two elements in the x, y, and z directions are: In the formula, β is the phase angle of the centroid, in rad; for the centrifugal force vector of the node, its equivalent force can be expressed as:

7. The fatigue life prediction method based on drill string dynamic stress according to claim 1, characterized in that, The specific content of step S3 includes: Displacement, velocity, acceleration, and external force vectors are the results of iterative solutions to the drill string dynamics control equations and are stored in [the relevant database / system]. In the four matrices {U} and {F}; Normal stress σ acting on the drill string x The shear stress τ is expressed as: In the formula, F x A represents the dynamic axial force borne by the drill string node, expressed in N (N). x M represents the cross-sectional area of ​​a drill string element, in meters (m). y M is the bending moment of the drill string at the y-axis section. z Let d be the bending moment of the drill string at the z-axis section. o d is the outer diameter of the drill string, in meters (m). i T0 is the inner diameter of the drill string, in meters (m); T0 is the torque acting on the drill string, in Nm; I y It is the moment of inertia along the y-axis, I z It is the moment of inertia along the z-axis.

8. The fatigue life prediction method based on drill string dynamic stress according to claim 7, characterized in that, Based on the Mohr stress circle criterion, the first principal stress σ1, the second principal stress σ2, and the third principal stress σ3 of the drill string are calculated. The equivalent stress expression at a certain location and time in the drill string is written as:

9. The fatigue life prediction method based on drill string dynamic stress according to claim 1, characterized in that, The specific content of step S4 includes: The continuous load-time history is discretized into a series of peaks and valleys using the rainflow counting method. The random load spectrum is obtained by performing cyclic counting statistical processing, and the mean stress and stress amplitude at each position of the drill string are obtained.

10. The fatigue life prediction method based on drill string dynamic stress according to claim 1, characterized in that, The content of step S5 is as follows: The general expression for the Goodman curve is: In the formula, S a S represents the stress amplitude. e For the fatigue limit, S m The mean stress, σ b For tensile strength and fatigue limit S e and tensile strength σ b It is determined by the properties of the material itself.

11. The fatigue life prediction method based on drill string dynamic stress according to claim 10, characterized in that, The equivalent mean of amplitude-mean-order under the Goodman curve is obtained by using the rainflow method, i.e., the stress amplitude S when the mean is 0. i : In the formula, S i S is the converted zero-mean stress amplitude. ai For the i-th stress amplitude, S mi Let σ be the mean stress value of the i-th stress. b Tensile strength.

12. The fatigue life prediction method based on drill string dynamic stress according to claim 1, characterized in that, The content of step S6 includes: The SN curve is obtained through fatigue experiments, where S represents the stress amplitude and N represents the number of cycles. S=2513.6N -0.132 (16) N=S -7.576 *2513.6 7.576 (17) Finally, the corrected zero-mean stress amplitude is substituted into the SN curve, and the fatigue life is solved using Miner's linear cumulative damage theory. Finally, combined with the calculation time, the service life of the drill string can be directly obtained.

13. The fatigue life prediction method based on drill string dynamic stress according to claim 12, characterized in that, When a material is subjected to stress cycles of varying amplitudes, each stress amplitude will cause damage to the material's fatigue life. The total fatigue damage of the material can be predicted by accumulating these damages; each stress amplitude S i The damage Di resulting from the corresponding number of cycles Ni is defined as: Where ni is the actual number of cycles the material undergoes under stress amplitude Si; The total damage D of the material is calculated using the following formula: When D = 1, the material reaches the critical state of failure or damage; when D < 1, the material has not yet reached fatigue failure. The service life P of the drill string is calculated using the following formula: P = D × t (20) In the formula, P is the service life of the drill string, and t is the calculation time.

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