A method and apparatus for suppressing drill string vibration during drilling based on modal analysis

Abstract

The application provides a drilling process drill string vibration suppression method and device based on modal analysis, relates to the field of geological drilling engineering, and comprises the following steps: S1, a drill string vibration model of a drill string system is constructed, the drill string vibration model comprises a drill string dynamics model and a drill bit-rock interaction model; S2, an external interference signal with a multi-modal characteristic is simulated and obtained through the drill bit-rock interaction model, and a main modal frequency of the external interference signal is extracted; and S3, an active suppression system is constructed by using an equivalent input interference method based on the drill string dynamics model and the main modal frequency, and the drill string vibration of the drill string system is suppressed through the active suppression system. The active suppression system is designed based on the drill string dynamics model and the main modal frequency, multi-modal disturbance caused by a multi-drill tool combination can be eliminated, stick-slip vibration phenomena generated in the drilling process can be effectively suppressed, and the drilling efficiency can be improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geological drilling engineering, and particularly relates to a drilling process drill string vibration suppression method and device based on modal analysis. BACKGROUND

[0002] The drill string system is an important tool for carrying out geological drilling, and is used as a hub to connect the surface drilling machine and the downhole drill bit, so as to transmit the driving torque on the well to the drill bit at the bottom of the well, and to apply pressure to the drill bit to break rocks. Therefore, the key to realizing safe and efficient geological drilling is how to drive the drill string to move and then drive the drill bit to extrude and twist to break rocks. With the continuous progress of the drilling process, the length of the drill string used can be thousands of meters, but the diameter is often less than 1 meter. Such a large length-diameter ratio makes the drill string have the physical characteristics of elastic deformation and rigid body motion coupling. Due to this structural characteristic of the drill string, the drill string is prone to vibration when driving the drill bit to break rocks, which makes the drill string vibration one of the most common and most prominent adverse phenomena in the geological drilling process. With the gradual increase of the drilling depth, the stratum changes become more and more complex, and the influence of the drill bit-rock interaction received by the drill bit at the bottom of the hole also becomes more and more intense. The influence of these factors often causes the drill string to produce stick-slip, drill bit rebound and other drill string vibration phenomena, which seriously affects the drilling efficiency and the service life of the drilling tools.

[0003] With the further increase of the drilling depth, the stratum changes affect the drill string vibration to exhibit a complex multi-modal and highly nonlinear motion state, which brings great difficulty to the control of the drilling process. Most of the existing control methods can only suppress the low-order modal of the drill string vibration, and the control effect on the high-order vibration modal of the drill string is generally poor, which leads to the fact that the designed controller cannot eliminate the drill string vibration in the actual deep geological drilling process. SUMMARY

[0004] Therefore, the present application aims to provide a drilling process drill string vibration suppression method and device based on modal analysis, which is used to solve the problem of stick-slip vibration of the drill string with multi-modal characteristics caused by the combination of multiple drilling tools in the current deep geological drilling process.

[0005] The present application provides a drilling process drill string vibration suppression method based on modal analysis, comprising:

[0006] S1: constructing a drill string vibration model of the drill string system, wherein the drill string vibration model comprises a drill string dynamics model and a drill bit-rock interaction model;

[0007] S2: obtaining an external disturbance signal with multi-modal characteristics by simulation through the drill bit-rock interaction model, and extracting the main modal frequency of the external disturbance signal;

[0008] S3: Based on the drill string dynamics model and the main modal frequency, an equivalent input disturbance method is used to construct an active suppression system, and the drill string system is suppressed by the active suppression system.

[0009] Preferably,

[0010] The expression of the drill string dynamics model is:

[0011]

[0012] wherein, θ p is the angular position of the top drive with 1 degree of freedom, θ pn is the angular position of the drill pipe with n degrees of freedom, θ h is the angular position of the weighted drill pipe with 1 degree of freedom, θ d is the angular position of the drill collar with 1 degree of freedom; is the input torque; is the reaction torque of the drill bit; is the given input channel; is the disturbance input channel; C a , J and are the local damping matrix, the inertia matrix and the torsional stiffness matrix, respectively;

[0013] The expression of the drill bit-rock interaction model is:

[0014]

[0015] wherein, W b is the weight on bit at the drill bit, R b is the drill bit radius, μ b is the dry friction coefficient.

[0016] Preferably,

[0017] Based on the drill string dynamics model, a state space equation from the input torque to the rotational speed output is constructed, and the state variable x is selected as:

[0018]

[0019] wherein, · represents the first order derivative with respect to time;

[0020] The expression of the state space equation is:

[0021]

[0022] wherein, x(t) is the state variable function, y(t) is the rotational speed of the top drive, u(t)=T1 is the control input, d(t)=T2 is the external disturbance signal, and A, B1, B2 and C are all state space matrices.

[0023] Preferably, step S2 is specifically:

[0024] S21: taking the reaction torque of the drill bit-rock interaction model as an external disturbance signal of the drill string system;

[0025] S22: decomposing the external disturbance signal into K-1 modal components and an untreated signal by a variational modal decomposition method;

[0026] S23: taking the component with the largest proportion in the modal components as a main modal, and extracting a main modal frequency.

[0027] Preferably:

[0028] The expression of the external disturbance signal d(t) is:

[0029]

[0030] where d k (t) is a modal component obtained by decomposition, d u (t) is an untreated signal.

[0031] Preferably, step S3 is specifically:

[0032] S31: constructing an observer The expression is:

[0033]

[0034] where · represents the first-order derivative of time, is the equivalent disturbance of the equivalent input disturbance estimation, L is the gain of the observer, K L is a gain factor;

[0035] The parameters of the observer are solved based on a linear matrix inequality method;

[0036] S32: constructing a state feedback, considering the internal model of the drill string system and the augmented state The state feedback is expressed as:

[0037]

[0038] where u(t) is a control input, d(t) is an external disturbance signal, A, B1, B2 and C are all state space matrices;

[0039] The parameters of the state feedback are solved based on a linear quadratic regulator;

[0040] S33: constructing a disturbance estimator, where the expression of the filter F(s) is:

[0041]

[0042] wherein T is a time constant;

[0043] The bandwidth of the filter is adjusted so that the disturbance estimator only covers the dominant modal frequencies of the decomposed disturbance;

[0044] S34: constructing an active suppression system by the observer, the state feedback and the disturbance estimator, and suppressing the drill string vibration of the drill string system by the active suppression system.

[0045] A storage medium, which stores instructions and data for implementing the drill string vibration suppression method in the drilling process based on modal analysis.

[0046] An equipment for suppressing drill string vibration in the drilling process based on modal analysis, comprising a processor and a storage medium; the processor loads and executes instructions and data in the storage medium to implement the drill string vibration suppression method in the drilling process based on modal analysis.

[0047] The present application has the following beneficial effects:

[0048] By constructing a drill string dynamics model to simulate stick-slip vibration of the drill string, an external interference signal is simulated by a bit-rock interaction model, a main modal frequency of the external interference signal is extracted by using a variational modal decomposition method, and an active suppression system is designed based on the drill string dynamics model and the main modal frequency, so that multi-modal disturbance caused by multi-drill tool assembly can be eliminated, stick-slip vibration phenomenon generated in the drilling process can be effectively suppressed, and drilling efficiency can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 The present application is an embodiment method flowchart;

[0050] Figure 2 The present application is a bit-rock interaction caused external interference signal diagram;

[0051] Figure 3 The present application is a main modal diagram extracted by twice variational modal decomposition of the external interference signal;

[0052] Figure 4 The present application is an active suppression system structure diagram;

[0053] Figure 5 The present application is an active suppression system control effect diagram;

[0054] Figure 6 The present application is an embodiment equipment structure diagram;

[0055] The implementation, functional features and advantages of the present application will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0056] It should be understood that the specific embodiments described herein are merely illustrative of the present application and do not limit the scope of the application.

[0057] With reference to Figure 1 , the present application provides a drilling process drill string vibration suppression method based on modal analysis, comprising:

[0058] S1: constructing a drill string vibration model of a drill string system, the drill string vibration model comprising: a drill string dynamics model and a drill bit-rock interaction model;

[0059] Further, based on an actual drill string system, in order to better study the stick-slip vibration of the drill string, a dynamics equation of the drill string in the torsion dimension is established; based on the analysis of rock breaking of the drill bit, a drill bit-rock interaction model is established, and the reaction torque caused by the drill bit-rock interaction is considered as an external disturbance signal of the drill string system.

[0060] The expression of the drill string dynamics model is:

[0061]

[0062] wherein, θ p is an angular position of the 1-DOF top drive, θ pn is an angular position of the n-DOF drill pipe, θ h is an angular position of the 1-DOF weighted drill pipe, θ d is an angular position of the 1-DOF drill collar; is an input torque; is a reaction torque borne by the drill bit; is a given input channel; is a disturbance input channel; C a , J and are respectively a local damping matrix, an inertia matrix and a torsional stiffness matrix;

[0063] The expression of the drill bit-rock interaction model is:

[0064]

[0065] wherein, W b is a bit pressure at the drill bit, R b is a drill bit radius, μ b is a dry friction coefficient.

[0066] Specifically, the dry friction coefficient can be expressed as:

[0067]

[0068] Ca , J and may be expressed as:

[0069]

[0070] Based on the relevant content of material mechanics, each item in the matrix is calculated by the following formula:

[0071]

[0072] where ∈ ∈ {pi, …, pn, h, d} represents the i-th (i ∈ 1…n) drill pipe unit, weighted drill pipe unit and drill collar; ρ and G s represent the density and shear modulus of the drill string; and I ∈ represent the outer diameter, inner diameter and polar moment of inertia about, respectively. is the drilling fluid damping coefficient per unit length of drill pipe; the inertia J p of the top drive is a constant.

[0073] According to the drill tool parameters of a well site in Xiangyang, Hubei, a torsional drill string vibration model is established, and the drill tool parameters are shown in Table 1.

[0074] Table 1 Drill string vibration simulation parameters

[0075]

[0076] Further, based on the drill string dynamics model, the state space equation from the input torque to the output speed is constructed, and the state variable x is selected as:

[0077]

[0078] where · represents the first order derivative with respect to time;

[0079] The expression of the state space equation is:

[0080]

[0081] where x(t) is the state variable function, y(t) is the speed of the top drive, u(t) = T1 is the control input, d(t) = T2 is the external disturbance signal, and A, B1, B2 and C are all state space matrices.

[0082] Specifically, the top drive and drill collar speeds are The disturbance signal is shown in Figure 2 .

[0083] S2: Through the drill bit-rock interaction model, the external disturbance signal with multi-modal characteristics is simulated to extract the main modal frequency of the external disturbance signal;

[0084] Further, step S2 is specifically:

[0085] S21: taking the reaction torque of the drill bit-rock interaction model as an external disturbance signal of the drill string system;

[0086] S22: decomposing the external disturbance signal into K-1 modal components and an untreated signal by a variational modal decomposition method;

[0087] S23: taking the component with the largest proportion in the modal components as a main modal, and extracting a main modal frequency.

[0088] Further, the expression of the external disturbance signal d(t) is:

[0089]

[0090] where d k (t) is a modal component obtained by decomposition, and d u (t) is an untreated signal.

[0091] S3: based on the drill string dynamics model and the main modal frequency, an active suppression system is constructed by using an equivalent input disturbance method, and the drill string system is suppressed by the active suppression system.

[0092] Further, an improved equivalent input disturbance method is used to determine the controller parameters based on the modal analysis results. The improved equivalent input disturbance method is used to suppress the external disturbance, the frequency of the equivalent disturbance is determined according to the extracted main modal frequency, the estimation accuracy of the disturbance is improved, the suppression of the disturbance is realized, and then the vibration suppression of the drill string system is realized.

[0093] Step S3 is specifically:

[0094] S31: constructing an observer The expression is:

[0095]

[0096] where · represents the first-order derivative of time, is an equivalent disturbance of the equivalent input disturbance estimation, L is the gain of the observer, and K L is a gain factor;

[0097] The parameters of the observer are solved based on a linear matrix inequality method;

[0098] Specifically, the equivalent disturbance of the equivalent input disturbance estimation can be expressed as:

[0099]

[0100] Then, the filtered disturbance estimate is given by F(s) and can be expressed as:

[0101]

[0102] where, and are the Laplace transforms of and respectively;

[0103] For the solution of the observer, the linear matrix inequality approach is used, and define:

[0104]

[0105] The state-space model of the vibration suppression system can be expressed as:

[0106]

[0107] where,

[0108]

[0109] Given four positive scalars a, b, x, g and a set of feedback control gains K, if there exists a symmetric positive definite matrix

[0110]

[0111] where,

[0112]

[0113] satisfy the following inequalities

[0114]

[0115] where,

[0116]

[0117] then the stability of the closed-loop system can be guaranteed, and the gain L of the observer and the gain factor KL can be expressed as:

[0118] L = -[I 0]P2 -1 W1,

[0119]

[0120] S32: Constructing the state feedback controller, considering the internal model of the drill string system and the augmented state State feedback controller is expressed as:

[0121]

[0122] wherein u(t) is the control input, d(t) is the external disturbance signal, A, B1, B2 and C are all state space matrices;

[0123] The parameters of the state feedback controller are solved based on a linear quadratic regulator;

[0124] Specifically, the objective function for solving the parameters of the state feedback controller is as follows:

[0125]

[0126] Q = diag{ones(1, 10), 100, ones(1, 10), 10}, R = 1

[0127] The state feedback gain can be expressed as:

[0128]

[0129] wherein P can be obtained by the following formula:

[0130]

[0131] S33: Construct a disturbance estimator, wherein the expression of the filter F(s) is:

[0132]

[0133] wherein T is a time constant;

[0134] Adjust the bandwidth of the filter so that the disturbance estimator only covers the main modal frequency of the decomposed disturbance;

[0135] Specifically, by analyzing the main modal of the extracted disturbance after decomposition, the frequency is concentrated in the range of 0.0015-1Hz, accounting for 89.5% of the entire vibration signal. The signal diagram of the decomposed external disturbance signal is as shown in Figure 3 Figure 3 As shown in (a), after one decomposition, the main modal still has a certain modal aliasing phenomenon, so secondary decomposition is performed to obtain Figure 3 (b). After analysis, it is found that the modal with frequency concentrated in the range of 0.0015-0.22Hz plays a main role, accounting for more than 90%.

[0136] Based on the modal analysis result, the bandwidth of the filter is adjusted so that it only covers the main modal frequency of the decomposed disturbance. Finally, the suppression of the disturbance with multi-modal characteristics is realized, and further the suppression of the drill string vibration is realized.

[0137] ​S34: Constructing an active suppression system by the observer, the state feedback and the disturbance estimator, and suppressing the drill string vibration of the drill string system through the active suppression system.

[0138] Specifically, by the idea of separation theorem, the observer and the state feedback are respectively designed to guarantee the stability of the system, and the structural block diagram of the active suppression system is as shown in the figure. Figure 4

[0139] The final control effect diagram is as shown in the figure. Figure 5 The system reaches the optimal control effect at T=0.7s, the system is out of the stick state at 15s, and reaches the steady state at 50s. Through the analysis of the simulation results, it is found that in the improved equivalent input disturbance method, the control effect can be significantly improved by adjusting the bandwidth of the filter, especially the time to reach the steady state. At the same time, although expanding the filter bandwidth can lead to unsatisfactory overall control effect, it can shorten the time for the drill string to first leave the stick stage during drilling and reduce the energy accumulation of the drill string, which also has significance for reducing the wear of the drilling tool.

[0140] Please refer to Figure 6 , Figure 6 is a hardware device working schematic diagram of the embodiment of the present application, and the hardware device specifically comprises: a drill string vibration suppression device in a drilling process based on modal analysis 401, a processor 402 and a storage medium 403.

[0141] The drill string vibration suppression device in a drilling process based on modal analysis 401: the drill string vibration suppression device in a drilling process based on modal analysis 401 realizes the drill string vibration suppression method in a drilling process based on modal analysis.

[0142] The processor 402: the processor 402 loads and executes the instructions and data in the storage medium 403 to realize the drill string vibration suppression method in a drilling process based on modal analysis.

[0143] The storage medium 403: the storage medium 403 stores instructions and data; the storage medium 403 is used to realize the drill string vibration suppression method in a drilling process based on modal analysis.

[0144] It should be noted that in this paper, the terms "include", "contain" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or system including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or system. Without more limitations, the element defined by the statement "including a" does not exclude the presence of another identical element in the process, method, article or system including the element. ​

[0145] The above-mentioned embodiment numbers of the present application are only for description, and do not represent the advantages and disadvantages of the embodiments. In the unit claims in which several devices are listed, several of the devices can be embodied by the same hardware item. The use of the words first, second, and third does not represent any order, and the words can be interpreted as identifiers.

[0146] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation, or direct or indirect application in other related technical fields, which is made by using the content of the specification and drawings of the present application, is also included in the patent protection scope of the present application.

Claims

1. A method for suppressing vibrations in a drill string during drilling operations based on modal analysis, characterized by, Comprising: S1: constructing a drill string vibration model of the drill string system, the drill string vibration model comprising: a drill string dynamics model and a bit-rock interaction model; S2: obtaining an external disturbance signal with multi-modal characteristics by simulation through the bit-rock interaction model, and extracting a main modal frequency of the external disturbance signal; Step S2 is specifically: S21: taking the reaction torque of the bit-rock interaction model as the external disturbance signal of the drill string system; S22: decomposing the external disturbance signal into K-1 modal components and an untreated signal by a variational modal decomposition method; S23: taking the component with the largest proportion in the modal components as the main modal, and extracting the main modal frequency; The expression of the external disturbance signal d(t) is: where d k (t) is the modal component obtained by decomposition, d u (t) is the unprocessed signal; S3: based on the drill string dynamics model and the main modal frequency, constructing an active suppression system by using an equivalent input disturbance method, and suppressing the drill string vibration of the drill string system through the active suppression system; Step S3 is specifically: S31: Constructing the observer The expression is: where • denotes the first derivative with respect to time, where L is the gain of the observer, K L is a gain factor; y(t) is the rotational speed of the top drive; Solving the parameters of the observer based on a linear matrix inequality method; S32: Construct a state feedback, considering the internal model of the drill string system and augmented state State feedback is represented as: Wherein, u(t) is the control input, d(t) is the external disturbance signal, A, B1, B2 and C are all state space matrices; x(t) is a state variable function; Solving the parameters of the state feedback by a linear quadratic regulator; S33: constructing a disturbance estimator, wherein the expression of the filter F(s) is: Wherein, T is a time constant; Adjust the bandwidth of the filter so that the disturbance estimator only covers the main modal frequency of the decomposed disturbance; S34: constructing an active suppression system by the observer, the state feedback and the disturbance estimator, and suppressing the drill string vibration of the drill string system through the active suppression system.

2. The drill string vibration suppression method for drilling process based on modal analysis according to claim 1, wherein: The expression of the drill string dynamics model is: wherein, θ p is the angular position of the top drive of 1 degree of freedom, θ pn is the angular position of the drill pipe of n degrees of freedom, θ h is the angular position of the weighted drill pipe of 1 degree of freedom, θ d is the angular position of the drill collar of 1 degree of freedom; is the input torque; is the reaction torque experienced by the drill bit; is the given input channel; is the disturbance input channel; C a , J and are the local damping matrix, the inertia matrix and the torsional stiffness matrix, respectively; The expression of the bit-rock interaction model is: where W b is the bit weight at the bit, R b is the bit radius, μ b is the dry friction coefficient.

3. The drill string vibration suppression method for drilling process based on modal analysis according to claim 2, wherein: Based on the drill string dynamics model, a state space equation from the input torque to the rotational speed output is constructed, and the state variable x is selected as: Wherein, · represents the first order derivative with respect to time; The expression of the state space equation is: Wherein, x(t) is a state variable function, y(t) is the rotational speed of the top drive, u(t)=T1 is the control input, d(t)=T2 is the external disturbance signal, A, B1, B2 and C are all state space matrices.

4. A storage medium characterized by: The storage medium stores instructions and data for realizing the drill string vibration suppression method for drilling process based on modal analysis according to any one of claims 1-3.

5. A drilling process string vibration suppression apparatus based on modal analysis, characterized by: Comprising: A processor and a storage medium; the processor loads and executes the instructions and data in the storage medium to realize the drill string vibration suppression method for drilling process based on modal analysis according to any one of claims 1-3.

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