A method for calculating the dynamic characteristics of a drill string under simple harmonic impact

Abstract

The application relates to a kind of calculation methods of the dynamic characteristics of drill string under simple harmonic impact, which comprises the following steps: one, drill pipe, collar, bottom hole assembly, drill bit are equivalent to two-degree-of-freedom axial and torsional coupling physical model of lumped mass;Two, based on the related theory of vibration mechanics, the mathematical model of two-degree-of-freedom axial and torsional coupling is described by Newton's theorem, and the mathematical model of drill string dynamics is established;Three, the mathematical model is modified by using state-dependent time delay method;Four, according to the dynamic characteristics of the drill string, the amplitude and angular frequency of the applied simple harmonic dynamic load are adjusted, and the dynamic characteristics of the drill string system are analyzed and determined.The application analyzes the influence of the amplitude and angular frequency of the applied simple harmonic impact on the dynamics of the drill string, which provides theoretical guidance for controlling the motion characteristics of the drill string, speeding up and reducing cost, and ensuring the safety of downhole.

Description

Technical fields:

[0001] This invention relates to the field of oil drilling technology, specifically to a method for calculating the dynamic characteristics of drill strings under harmonic impact. Background technology:

[0002] In recent years, my country's petroleum industry has developed rapidly in terms of production capacity and scale. As an important means of petroleum exploration and development, the development of drilling technology and the research of corresponding theories are of great significance to my country's petroleum industry.

[0003] Current drilling engineering development shows a surge in the number of deep and ultra-deep wells. With increasing depth, the drill string can no longer be considered a rigid body, making it more prone to stick-slip, drill-skip issues, and even chaotic phenomena. Twisting stick-slip vibrations can lead to premature fatigue failure of downhole drilling tools; axial drill-skip issues significantly reduce drilling efficiency and increase costs. Therefore, to effectively avoid stick-slip and drill-skip problems, improve the rate of penetration (ROP), reduce drilling costs, and ensure drilling safety, it is necessary to analyze the dynamic characteristics of the drill string.

[0004] Currently, research on drill string dynamics mainly focuses on torsional vibration and shaft-torsional combined vibration. The study of torsional vibration primarily investigates the stick-slip effect in the torsional direction. This method is based on vibration dynamics theory, using the Hamiltonian principle and Lagrange's equations to establish a dynamic model and analyze the influence of relevant parameters on angular velocity and angular displacement. The study of shaft-torsional combined vibration, based on torsional vibration, considers axial vibration, in which the drill pressure and torque acting on the drill bit are coupled.

[0005] However, existing research methods are only applicable to the most primitive percussion drilling techniques. With the continuous development of drilling technology, many scholars have proposed new methods and tools for efficient rock breaking, such as resonant drilling and hydraulic oscillators, bringing harmonic percussion technology into the view of drilling professionals. Therefore, research on drilling dynamics cannot stagnate; a method is urgently needed to analyze drill string dynamics under harmonic percussion that aligns with current advancements in efficient rock breaking. Summary of the Invention:

[0006] The purpose of this invention is to provide a method for calculating the dynamic characteristics of drill strings under harmonic impact. This method is used to solve the problem of low rock breaking efficiency in current torsional vibration and shaft-torsional composite vibration methods.

[0007] The technical solution adopted by this invention to solve its technical problem is: a method for calculating the dynamic characteristics of drill strings under simple harmonic impact.

[0008] Step 1: Equip the drill pipe, drill collar, bottom drill assembly, and drill bit with a concentrated mass and a two-degree-of-freedom physical model that couples axial and torsional forces.

[0009] Step 2: Based on the relevant theories of vibration dynamics, Newton's theorem is used to describe the mathematical model of the two-degree-of-freedom axial and torsional coupling, and the mathematical model of the axial-torsional composite dynamics under harmonic impact is established as follows:

[0010]

[0011]

[0012] In the formula Angular acceleration, Φ is angular velocity, C is angular displacement. t For the torsional damping coefficient, K t Ω0 is the torsional stiffness coefficient, T is the rotary table speed, and T is the torque on the drill bit. Axial acceleration, X is the axial velocity, C is the axial displacement, and C is the axial velocity. a For axial damping coefficient, K a denoted as axial stiffness coefficient, v0 as hook movement speed, W0 as steady-state drill pressure, W as drill pressure on the drill bit, F0 as applied harmonic impact amplitude, and w as applied harmonic impact frequency.

[0013] Step 3: The mathematical model of axial-torsional composite dynamics under harmonic impact is modified by using the state-dependent time hysteresis method.

[0014] Step 4: Based on the drill string dynamic characteristics, adjust the amplitude and angular frequency of the applied simple harmonic dynamic load, and analyze and determine the dynamic characteristics of the drill string system.

[0015] The method for obtaining T and W in step two of the above scheme is as follows:

[0016] Taking compliance into account, the drilling pressure and torque are:

[0017]

[0018]

[0019] In the formula, T c For the torque cutting component; T f W represents the torque friction component. c W is the drilling pressure cutting component; f d represents the drill pressure friction component; d represents the drill bit cutting depth. Let be a unit step function of angular velocity. H(d) is a unit step function with respect to axial velocity, and H(d) is a unit step function with respect to depth of cut. For the sign function of angular velocity, Let be a sign function for axial velocity and sgn(d) be a sign function for depth of cut, defined as follows:

[0020] T c =0.5εR b nd n T f =0.5R b 2 γμlσ

[0021] W c =ξεR b nd n W f =R b lσ

[0022]

[0023]

[0024] In the formula, ε is the specific energy of rock fragmentation, and R b Let n be the drill bit radius, n be the number of drill bit blades, and d be the number of drill bit blades. n Let ξ be the vertical cutting depth for each blade, γ be a parameter related to the direction of the cutting force, γ be a geometric characteristic parameter of the drill bit greater than 1, μ be the coefficient of friction, l be the length of the drill bit wear plane, and σ be the contact stress.

[0025] In the above scheme, the vertical cutting depth of each blade is determined by the axial displacement X(t) and the state-dependent time-delay variable t. n t n The axial displacement X(tt) before n The results are calculated using the time variable t:

[0026] d n =X(t)-X(tt) n )

[0027] In the above scheme, the state-dependent time-delay method depends on the time-delay variable t. n The result is obtained from the following expression:

[0028]

[0029] Where Φ(t) and Φ(tt) n ) are angular displacement and t respectively n The angular displacement before.

[0030] The beneficial effects of this invention are as follows:

[0031] 1. This invention treats the drill pipe, drill collar, BHA, and drill bit as equivalent concentrated masses. Based on vibration dynamics theory, it establishes an axial-torsional two-degree-of-freedom dynamic model under harmonic impact, conforming to the development of efficient rock breaking. The model is modified to consider compliance. To better reflect actual engineering conditions, a state-dependent time-delay variable is introduced, and a more accurate fourth-order Runge-Kutta method is used for drill string dynamics analysis.

[0032] 2. This invention analyzes the influence of external harmonic impact amplitude and angular frequency on drill string dynamics, providing theoretical guidance for controlling drill string motion characteristics, increasing speed and reducing costs, and ensuring downhole safety.

[0033] 3. The torsional vibration model and the shaft-torsion composite model cannot effectively analyze the dynamic characteristics of drill strings that conform to the development of efficient rock breaking. This invention provides a method for analyzing the complex dynamic characteristics of downhole drill strings under harmonic impact. By establishing a state-dependent time-delay dynamic model with two degrees of freedom in the axial and torsional directions, considering the amplitude and frequency of the applied harmonic dynamic load, the problem is analyzed using the fourth-order Runge-Kutta method. Attached Figure Description

[0034] Figure 1 This is a diagram of the axial vibration model of the drill string dynamics system.

[0035] Figure 2 This is a diagram of the torsional vibration model of the drill string dynamics system.

[0036] Figure 3 The graph shows the effect of different angular frequencies on angular velocity.

[0037] Figure 4 The graph shows the effect of different angular frequencies on axial velocity.

[0038] Figure 5 The graph shows the effect of different amplitudes on angular velocity;

[0039] Figure 6 This is a graph showing the effect of different amplitudes on axial velocity. Detailed implementation method:

[0040] The invention will be further described below with reference to the accompanying drawings:

[0041] The calculation method for the dynamic characteristics of drill string under simple harmonic impact:

[0042] Step 1: Equip the drill pipe, drill collar, bottom drill assembly, and drill bit with a concentrated mass and a two-degree-of-freedom physical model that couples axial and torsional forces.

[0043] Step 2: Based on the relevant theories of vibration dynamics, Newton's theorem is used to describe the mathematical model of the two-degree-of-freedom axial and torsional coupling, thus establishing the drill string dynamics mathematical model:

[0044] The mathematical model of axial-torsional composite dynamics under harmonic impact is as follows:

[0045]

[0046]

[0047] In the formula Angular acceleration, Φ is angular velocity, C is angular displacement. t For the torsional damping coefficient, K t Ω0 is the torsional stiffness coefficient, T is the rotary table speed, and T is the torque on the drill bit. Axial acceleration, X is the axial velocity, C is the axial displacement, and C is the axial velocity. a For axial damping coefficient, K a denoted as axial stiffness coefficient, v0 as hook movement speed, W0 as steady-state drill pressure, W as drill pressure on the drill bit, F0 as applied harmonic impact amplitude, and w as applied harmonic impact frequency.

[0048] Taking compliance into account, drilling pressure and torque are written as follows:

[0049]

[0050]

[0051] In the formula, T c For the torque cutting component; T f W represents the torque friction component. c W is the drilling pressure cutting component; f d represents the drill pressure friction component; d represents the drill bit cutting depth. Let be a unit step function of angular velocity. H(d) is a unit step function with respect to axial velocity, and H(d) is a unit step function with respect to depth of cut. For the sign function of angular velocity, Let be a sign function for axial velocity and sgn(d) be a sign function for depth of cut, defined as follows:

[0052] T c =0.5εR b nd n T f =0.5R b 2 γμlσ

[0053] W c =ξεR b nd n Wf =R b lσ

[0054]

[0055]

[0056] In the formula, ε is the specific energy of rock fragmentation, and R b Let n be the drill bit radius, n be the number of drill bit blades, and d be the number of drill bit blades. n Let ξ be the vertical cutting depth for each blade, γ be a parameter related to the direction of the cutting force, γ be a geometric characteristic parameter of the drill bit greater than 1, μ be the coefficient of friction, l be the length of the drill bit wear plane, and σ be the contact stress.

[0057] d n =X(t)-X(tt) n ).

[0058] Step 3: The solution of the conventional drill string system dynamic model is based on the assumption of a fixed cutting depth of the drill bit. In order to more realistically and in real time reflect the actual rock breaking movement of the drill bit at the bottom of the well, the state-dependent time lag method is used to modify the mathematical model.

[0059] State-dependent time-delay variable t n The result is obtained from the following expression:

[0060]

[0061] Step 4: Based on the drill string dynamic characteristics, adjust the amplitude and angular frequency of the applied simple harmonic dynamic load, and analyze and determine the dynamic characteristics of the drill string system.

[0062] Figure 1 This is a schematic diagram of the physical model of the drill string system. In order to better study the dynamic characteristics of the drill string, the following assumptions were made when establishing the drill string dynamic model:

[0063] (1) The drill string system has no horizontal movement;

[0064] (2) Both the wellbore and the drill string system are in a vertical state, and the axis of each component of the drill string system always coincides with the axis of the wellbore.

[0065] (3) The drill string dynamics system does not contain downhole power drilling tools and is rotary table driven;

[0066] (4) Wear of components such as drill bits is not considered.

[0067] Let Z1 = Φ, Z3 = X, U1(t) = -T + K t Ω0t, U2=F0cos(wt)+W0-W+Ka v0t, the writing matrix form is as follows:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] The dynamic equations are solved using the fourth-order Runge-Kutta method:

[0074] k1 = AZ i +BU

[0075]

[0076]

[0077] k4=A(Z i +hk3)+BU

[0078]

[0079] In the formula, h is the step size, which is generally taken as 10⁻⁴-10⁻⁵, and k i This is the Runge-Kutta coefficient matrix.

[0080] like Figure 2 As shown, the angular velocity curves are at different frequencies. When the frequency is low, the angular velocity curve changes more regularly. When the frequency is high, the angular velocity periodically reaches 0, and stick-slip vibration occurs in the torsional direction.

[0081] like Figure 3 As shown, the axial velocity curves are at different frequencies. When the frequency is low, the axial velocity curve changes more regularly. When the frequency is high, the axial velocity becomes negative, and skipping occurs in the axial direction.

[0082] like Figure 4 As shown, the angular velocity curves are for different amplitudes. When the amplitude is small, the angular velocity curve changes more regularly. When the amplitude is large, the angular velocity periodically reaches 0, and stick-slip vibration occurs in the torsional direction.

[0083] like Figure 5 As shown, the axial velocity curves are under different amplitudes. When the amplitude is small, the axial velocity curve changes more regularly. When the amplitude is large, the axial velocity becomes negative, and drilling skips in the axial direction.

[0084] In summary, the amplitude and frequency of harmonic impact have a significant impact on drill string dynamics. In practical engineering, excessively high amplitude and excessively low frequency will both have adverse effects on drill string dynamics. Therefore, adjusting the amplitude and frequency of the harmonic impact to maximize rock-breaking efficiency is highly feasible in actual drilling operations.

[0085] To analyze the dynamic characteristics of the drill string, it is necessary to establish corresponding dynamic equations. Current research on drill string dynamics mostly focuses on the stick-slip effect in the torsional direction. This approach is sufficient for traditional percussion drilling. However, in addition to stick-slip in the torsional direction, the axial direction can also experience drill skipping, which similarly reduces mechanical speed and increases drilling cycle time. In recent years, with the development of new high-efficiency rock-breaking technologies, studying only stick-slip vibration in the torsional direction is insufficient to address more complex problems. Therefore, this invention employs a two-degree-of-freedom dynamic model in both the axial and torsional directions, which better reflects the real-world situation.

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method of calculating the dynamic behavior of a drill string under simple harmonic shock, characterized in that The method comprises the following steps: Step one, the drill pipe, drill collar, bottom hole assembly, drill bit are equivalent to a two-degree-of-freedom axial and torsional coupling physical model of concentrated mass; Step two, based on the related theory of vibration mechanics, the two-degree-of-freedom axial and torsional coupling mathematical model is described by Newton's theorem, and an axial-torsional composite dynamic mathematical model under simple harmonic impact is established as follows: ； ； wherein is the angular acceleration, is the angular velocity, ф is the angular displacement, Ct is the torsional damping coefficient, Kt is the torsional stiffness coefficient, Ω0 is the rotary table speed, T is the torque on the bit, is the axial acceleration, is the axial velocity, X is the axial displacement, Ca is the axial damping coefficient, Ka is the axial stiffness coefficient, v0 is the hook speed, W0 is the steady-state weight on bit, W is the weight on bit, F0 is the amplitude of the applied harmonic shock, and ω is the frequency of the applied harmonic shock. The method for solving T and W is as follows: ； ； where Tc is the torque cutting component; T f is the torque friction component; Wc is the weight on bit cutting component; W f is the weight on bit friction component; d is the bit depth of cut; is a unit step function in angular velocity, is a unit step function in axial velocity, H(d) is a unit step function in depth of cut; is a sign function in angular velocity, respectively defined as: ； ； ； ； where ε is the specific energy of rock breakage, R b is the radius of the drill bit, n is the number of blades of the drill bit, dn is the vertical depth of cut of each blade, is the parameter related to the direction of cutting force, γ is the drill bit geometry parameter greater than 1, µ is the friction coefficient, l is the length of the drill bit wear flat, σ is the contact stress; The vertical depth of cut of each blade is calculated from the axial displacement X(t) and the state-dependent time lag variable t n , n X(t-t n ) and the time variable t ； Step three, the state-dependent time delay method is used to modify the axial-torsional combined dynamic mathematical model under simple harmonic impact; the state-dependent time delay variable t n is obtained according to the following expression: ； where φ(t), φ(t - t n ) are the angular displacement and the angular displacement before t n , respectively. Step four, according to the drill string dynamic characteristics, the amplitude and angular frequency of the external simple harmonic dynamic load are adjusted, and the drill string system dynamic characteristics are analyzed and determined.

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