CN108984872B - Method for analyzing and evaluating motion of oscillator in casing mud and effect of oscillator on casing - Google Patents

Method for analyzing and evaluating motion of oscillator in casing mud and effect of oscillator on casing Download PDF

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CN108984872B
CN108984872B CN201810702491.2A CN201810702491A CN108984872B CN 108984872 B CN108984872 B CN 108984872B CN 201810702491 A CN201810702491 A CN 201810702491A CN 108984872 B CN108984872 B CN 108984872B
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oscillator
collision
casing
sleeve
formula
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CN108984872A (en
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刘延强
赵德敏
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China University of Petroleum East China
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Abstract

The invention relates to a method for analyzing and evaluating the main motion behavior of an oscillator in casing mud and the effect of the oscillator on a casing, which comprises the following steps of starting the oscillator, calculating and recording the occurrence time t through a motion equation 1 To get solved
Figure DDA0001714804110000011
The movement of the oscillator is the movement of the oscillator before collision and the residual vibration generated by the collision of the sleeve
Figure DDA0001714804110000012
Or
Figure DDA0001714804110000013
Time, calculating the occurrence time t of recording from the time motion equation 2 To get solved
Figure DDA0001714804110000014
To be provided with
Figure DDA0001714804110000015
Or
Figure DDA0001714804110000017
The residual vibration generated by sleeve collision is superposed in the motion equation as an initial condition, and by analogy, the time, initial angular velocity and collision impulse t of each sleeve collision are solved i 、
Figure DDA0001714804110000018
So as to finally obtain a series of oscillator pair sleeves
Figure DDA0001714804110000019
Or
Figure DDA00017148041100000110
Action time and impact impulse t i 、 Ii (ii) a The method has the advantages that the method can effectively analyze and evaluate the main motion behavior of the oscillator in the casing mud and the effect of the oscillator on the casing and provide data support for analyzing the effect of the casing on the cement slurry.

Description

套管泥浆中振荡器的运动及其对套管作用的分析评估方法Analysis and evaluation method of the movement of oscillators in casing mud and its effect on casing

技术领域Technical Field

本发明属于钻井技术领域，涉及套管泥浆中振荡器的运动及其对套管的作用分析评估方法。The invention belongs to the technical field of drilling, and relates to a method for analyzing and evaluating the movement of an oscillator in casing mud and its effect on the casing.

背景技术Background Art

在钻井完井过程中，灌注水泥固实套管的质量将直接影响着完井后套管的工作质量。若固井水泥分布不均匀不密实，就会造成套管受力不均匀而易于发生破损。因此，灌注水泥如何达到均匀密实的效果，一直是完井工作者关心的问题。为此，人们设计了不同的振荡器下入套管中，以图通过振荡器的摆动冲击套管激起套管振动进而促使套管外水泥波动，达到固井水泥分布均匀密实效果。但对此缺乏理论分析验证支撑，资料少见。本文试图通过对振荡器在直井套管中的运动和对套管的作用主要行为，进行模拟分析，探索分析振荡器对套管水泥固实效果的评估方案。During the drilling and completion process, the quality of cementing the casing will directly affect the working quality of the casing after completion. If the cementing cement is unevenly distributed and not dense, the casing will be unevenly stressed and prone to damage. Therefore, how to achieve a uniform and dense effect when pouring cement has always been a concern for completion workers. To this end, people have designed different oscillators to be lowered into the casing in an attempt to stimulate the casing vibration through the oscillator's swing and impact the casing, thereby causing the cement outside the casing to fluctuate, so as to achieve a uniform and dense distribution of cement. However, there is a lack of theoretical analysis and verification support for this, and there is little data. This paper attempts to simulate and analyze the movement of the oscillator in the casing of a vertical well and the main behavior of its action on the casing, and explore and analyze the evaluation scheme of the oscillator on the cement consolidation effect of the casing.

发明内容Summary of the invention

本发明的目的在于提供套管泥浆中振荡器的运动及其对套管作用的分析评估方法，本发明的有益效果是能够确定套管泥浆中振荡器的主要运动行为及其对套管的作用效果。The purpose of the present invention is to provide an analytical evaluation method for the movement of an oscillator in casing mud and its effect on casing. The beneficial effect of the present invention is that the main movement behavior of the oscillator in casing mud and its effect on casing can be determined.

本发明所采用的技术方案是按照以下步骤进行：The technical solution adopted by the present invention is carried out according to the following steps:

(1)从振荡器启动开始，运动方程为式(1)，当

Figure BDA0001714804090000011
或
Figure BDA0001714804090000012
时(正负取决于式(1)此时的计算结果)，由式(1)试算出与套管第一次碰撞时间t1，由式(6)、式(5)解得与套管第一次碰撞后角速度
Figure BDA0001714804090000013
和碰撞冲量I，记为
Figure BDA0001714804090000014
I1，碰撞时角位移为
Figure BDA0001714804090000015
或
Figure BDA0001714804090000016
(1) Starting from the start of the oscillator, the motion equation is (1), when
Figure BDA0001714804090000011
or
Figure BDA0001714804090000012
When (the positive or negative value depends on the calculation result of formula (1) at this time), the first collision time t1 with the casing is calculated by formula (1), and the angular velocity after the first collision with the casing is obtained by solving formula (6) and formula (5):
Figure BDA0001714804090000013
and the collision impulse I, denoted as
Figure BDA0001714804090000014
I 1 , the angular displacement during collision is
Figure BDA0001714804090000015
or
Figure BDA0001714804090000016

(2)以

Figure BDA0001714804090000017
为初始条件，振荡器与套管第一次碰撞后的运动方程为式(7)。当
Figure BDA0001714804090000018
或
Figure BDA0001714804090000019
时(正负取决于式(7)此时的计算结果)，由式(7)试算出与套管第二次碰撞时间t2，由式(8)、式(5)解得与套管第二次碰撞后角速度
Figure BDA00017148040900000110
和碰撞冲量I，记为
Figure BDA00017148040900000111
I2，碰撞时角位移为
Figure BDA00017148040900000112
或
Figure BDA00017148040900000113
(2)
Figure BDA0001714804090000017
As the initial condition, the motion equation after the first collision between the oscillator and the casing is equation (7).
Figure BDA0001714804090000018
or
Figure BDA0001714804090000019
When (the positive or negative value depends on the calculation result of formula (7) at this time), the second collision time t2 with the casing is calculated by formula (7), and the angular velocity after the second collision with the casing is obtained by solving formula (8) and formula (5):
Figure BDA00017148040900000110
and the collision impulse I, denoted as
Figure BDA00017148040900000111
I 2 , the angular displacement during collision is
Figure BDA00017148040900000112
or
Figure BDA00017148040900000113

(3)以此类推。在获得第i-1次碰撞后的ti-1,

Figure BDA0001714804090000021
Ii-1后，以
Figure BDA0001714804090000022
为初始条件，振荡器与套管第i-1次碰撞后的运动方程为式(10)，由
Figure BDA0001714804090000023
或
Figure BDA0001714804090000024
(正负取决于式(10)此时的计算结果)与式(10)试算法解得初始到第i次撞击套管经历的时间刻ti。碰撞时角位移为
Figure BDA0001714804090000025
或
Figure BDA0001714804090000026
由式(11)、式(5)解得与套管第i次碰撞后角速度
Figure BDA0001714804090000027
和碰撞冲量I，记为
Figure BDA0001714804090000028
Ii。(3) And so on. After obtaining the i-1th collision t i-1 ,
Figure BDA0001714804090000021
After I i-1 ,
Figure BDA0001714804090000022
As the initial condition, the motion equation after the oscillator and the casing collide for the i-1th time is (10), which is given by
Figure BDA0001714804090000023
or
Figure BDA0001714804090000024
(The positive or negative value depends on the calculation result of formula (10) at this time) and formula (10) are used to solve the time t i from the initial to the i-th impact on the casing. The angular displacement at the time of collision is
Figure BDA0001714804090000025
or
Figure BDA0001714804090000026
The angular velocity after the i-th collision with the casing is obtained by solving equations (11) and (5):
Figure BDA0001714804090000027
and the collision impulse I, denoted as
Figure BDA0001714804090000028
I i .

如此最终获得一系列振荡器对套管的作用时间与碰撞冲量ti、Ii；据此评估振荡器对套管的作用情况，如撞击强度和频率(通过ti确定各相邻碰撞间隔时间，然后平均统计出碰撞周期、频率)。In this way, a series of oscillator action time and collision impulse ti , Ii on the casing are finally obtained; based on this, the action of the oscillator on the casing, such as the impact intensity and frequency, is evaluated (the interval between adjacent collisions is determined by ti , and then the collision cycle and frequency are averaged and counted).

其中，套管中的振荡器的运动受到套管的限制，当横向位移达到振荡器外半径与套管内半径差时，就会与套管发生碰撞，与套管发生碰撞时，振荡器达到最大角位移为The movement of the oscillator in the casing is restricted by the casing. When the lateral displacement reaches the difference between the outer radius of the oscillator and the inner radius of the casing, it will collide with the casing. When colliding with the casing, the oscillator reaches a maximum angular displacement of

Figure BDA0001714804090000029
Figure BDA0001714804090000029

式中，D1为套管内径，l为振荡器长度，D为振荡器外筒外径，l1为振荡器顶部离悬点O的距离，α为振荡器底部形心和与套管接触点分别与悬点O的连线间夹角。Where D1 is the inner diameter of the casing, l is the length of the oscillator, D is the outer diameter of the outer tube of the oscillator, l1 is the distance between the top of the oscillator and the suspension point O, and α is the angle between the centroid of the bottom of the oscillator and the line connecting the contact point with the casing and the suspension point O.

振荡器开动前，振荡器静止，角位移

Figure BDA00017148040900000210
角速度
Figure BDA00017148040900000211
即初始条件为
Figure BDA00017148040900000212
振荡器运动方程为Before the oscillator is started, the oscillator is stationary and the angular displacement
Figure BDA00017148040900000210
Angular velocity
Figure BDA00017148040900000211
That is, the initial condition is
Figure BDA00017148040900000212
The equation of motion for the oscillator is

Figure BDA00017148040900000213
Figure BDA00017148040900000213

式中，ξ为振荡器系统的阻尼比，p为振荡器系统的固有频率，

Figure BDA00017148040900000214
为振荡器的衰减固有频率，ω为振荡器转子转动角速度，α0为振荡器系统稳态响应初相位，Φ为振荡器系统稳态响应振幅。Where ξ is the damping ratio of the oscillator system, p is the natural frequency of the oscillator system,
Figure BDA00017148040900000214
is the attenuated natural frequency of the oscillator, ω is the angular velocity of the oscillator rotor, α0 is the initial phase of the steady-state response of the oscillator system, and Φ is the amplitude of the steady-state response of the oscillator system.

设振荡器与套管发生碰撞恢复系数为k，则Assume that the recovery coefficient of the collision between the oscillator and the casing is k, then

Figure BDA0001714804090000031
Figure BDA0001714804090000031

式中，v1、u1分别为碰撞前后振荡器与套管接触点的速度，则Where v 1 and u 1 are the velocities of the contact point between the oscillator and the casing before and after the collision, respectively.

Figure BDA0001714804090000032
Figure BDA0001714804090000032

式中，

Figure BDA0001714804090000033
分别为碰撞前后振荡器在x1z1平面内的角速度，代入式(2)有In the formula,
Figure BDA0001714804090000033
are the angular velocities of the oscillator in the x 1 z 1 plane before and after the collision, respectively. Substituting them into equation (2), we have

Figure BDA0001714804090000034
Figure BDA0001714804090000034

对于皆为钢制的振荡器与套管的碰撞恢复系数可查知k＝0.56。For the collision recovery coefficient of the oscillator and the sleeve, both of which are made of steel, it can be found that k=0.56.

根据冲量矩定理，有According to the impulse moment theorem, we have

Figure BDA0001714804090000035
Figure BDA0001714804090000035

式中，I为套管作用于振荡器的冲量，JO为振荡器系统对O轴的转动惯量。Where I is the impulse of the casing acting on the oscillator, and J O is the moment of inertia of the oscillator system about the O-axis.

由式(3)、(4)解得From equations (3) and (4), we can get

Figure BDA0001714804090000036
Figure BDA0001714804090000036

由

Figure BDA0001714804090000037
或
Figure BDA0001714804090000038
与式(1)采用试算法解得初始到第一次撞击套管经历的时间t1，第一次撞击套管时的角位移与角速度分别为Depend on
Figure BDA0001714804090000037
or
Figure BDA0001714804090000038
The time t 1 from the initial impact to the first impact on the casing is obtained by trial and error with equation (1). The angular displacement and angular velocity when the casing is first impacted are:

Figure BDA0001714804090000039
Figure BDA0001714804090000039

由式(5)、式(6)解得第一次碰撞后角速度

Figure BDA00017148040900000310
和碰撞冲量I，记为
Figure BDA00017148040900000311
I1。振荡器受到碰撞后，将以
Figure BDA00017148040900000312
为初始条件，运动方程为The angular velocity after the first collision is obtained by solving equations (5) and (6):
Figure BDA00017148040900000310
and the collision impulse I, denoted as
Figure BDA00017148040900000311
I 1. After the oscillator is hit, it will
Figure BDA00017148040900000312
is the initial condition, and the equation of motion is

Figure BDA00017148040900000313
Figure BDA00017148040900000313

由

Figure BDA00017148040900000314
或
Figure BDA00017148040900000315
与式(7)试算法解得初始到第二次撞击套管经历的时间刻t2，第二次撞击套管时的角位移与角速度分别为Depend on
Figure BDA00017148040900000314
or
Figure BDA00017148040900000315
The time t 2 from the initial impact to the second impact on the casing is obtained by trial calculation with equation (7). The angular displacement and angular velocity at the second impact on the casing are

Figure BDA00017148040900000316
Figure BDA00017148040900000316

Figure BDA0001714804090000041
Figure BDA0001714804090000041

由式(5)、式(8)解得第二次碰撞后角速度

Figure BDA00017148040900000415
和碰撞冲量I，记为
Figure BDA0001714804090000042
I2。振荡器受到第二次碰撞后，将以
Figure BDA0001714804090000043
为初始条件，运动方程为The angular velocity after the second collision is obtained by solving equations (5) and (8):
Figure BDA00017148040900000415
and the collision impulse I, denoted as
Figure BDA0001714804090000042
I 2. After the oscillator is hit for the second time, it will
Figure BDA0001714804090000043
is the initial condition, and the equation of motion is

Figure BDA0001714804090000044
Figure BDA0001714804090000044

以此类推。在获得第i-1次碰撞后的ti-1,

Figure BDA0001714804090000045
Ii-1后，以
Figure BDA0001714804090000046
为初始条件，运动方程为And so on. After obtaining the i-1th collision, t i-1 ,
Figure BDA0001714804090000045
After I i-1 ,
Figure BDA0001714804090000046
is the initial condition, and the equation of motion is

Figure BDA0001714804090000047
Figure BDA0001714804090000047

由

Figure BDA0001714804090000048
或
Figure BDA0001714804090000049
与式(10)试算法解得初始到第i次撞击套管经历的时间刻ti，第i次撞击套管时的角位移和角速度分别为Depend on
Figure BDA0001714804090000048
or
Figure BDA0001714804090000049
The time from the initial impact to the ith impact on the casing is obtained by trial calculation with equation (10) as t i . The angular displacement and angular velocity at the ith impact on the casing are

Figure BDA00017148040900000410
Figure BDA00017148040900000410

由式(5)、式(11)解得第i次碰撞后角速度

Figure BDA00017148040900000411
和碰撞冲量I，记为
Figure BDA00017148040900000412
Ii。振荡器受到碰撞后，将以
Figure BDA00017148040900000413
为初始条件，运动方程为The angular velocity after the i-th collision is obtained by solving equations (5) and (11):
Figure BDA00017148040900000411
and the collision impulse I, denoted as
Figure BDA00017148040900000412
I i . After the oscillator is hit, it will
Figure BDA00017148040900000413
is the initial condition, and the equation of motion is

Figure BDA00017148040900000414
Figure BDA00017148040900000414

由此，确定套管中振荡器的运动行为和对套管的作用状况。Thus, the movement behavior of the oscillator in the casing and the effect on the casing are determined.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1是振激器与套管接触碰撞示意图。FIG. 1 is a schematic diagram of the contact and collision between the vibrator and the casing.

具体实施方式DETAILED DESCRIPTION

下面结合具体实施方式对本发明进行详细说明。The present invention is described in detail below in conjunction with specific implementation modes.

套管中的振荡器的运动受到套管的限制，当横向位移达到振荡器外半径与套管内半径差(简称视半径)时，就会与套管发生碰撞。属于边界非线性振动问题。设套管内径为D1，振荡器与套管发生碰撞时，由图1所示。The movement of the oscillator in the casing is restricted by the casing. When the lateral displacement reaches the difference between the outer radius of the oscillator and the inner radius of the casing (referred to as the apparent radius), it will collide with the casing. This is a boundary nonlinear vibration problem. Assuming the inner diameter of the casing is D 1 , when the oscillator collides with the casing, as shown in Figure 1.

Figure BDA0001714804090000051
Figure BDA0001714804090000051

振荡器开动前，

Figure BDA0001714804090000052
即
Figure BDA0001714804090000053
Before the oscillator starts,
Figure BDA0001714804090000052
Right now
Figure BDA0001714804090000053

Figure BDA0001714804090000054
Figure BDA0001714804090000054

式中，ξ为振荡器系统的阻尼比，p为振荡器系统的固有频率，

Figure BDA0001714804090000055
为振荡器的衰减固有频率，ω为振荡器转子转动角速度，α0为振荡器系统稳态响应初相位，Φ为振荡器系统稳态响应振幅。Where ξ is the damping ratio of the oscillator system, p is the natural frequency of the oscillator system,
Figure BDA0001714804090000055
is the attenuated natural frequency of the oscillator, ω is the angular velocity of the oscillator rotor, α0 is the initial phase of the steady-state response of the oscillator system, and Φ is the amplitude of the steady-state response of the oscillator system.

设振荡器与套管发生碰撞恢复系数为k。考虑碰撞前后套管上撞击点的横向速度与振荡器撞击点的横向速度相比要小得多，由碰撞理论，近似有Assume that the coefficient of restitution when the oscillator collides with the casing is k. Considering that the lateral velocity of the impact point on the casing before and after the collision is much smaller than the lateral velocity of the impact point on the oscillator, according to the collision theory, we can approximate

Figure BDA0001714804090000056
Figure BDA0001714804090000056

式中，v1、u1分别为碰撞前后振荡器与套管接触点的速度。则Where v 1 and u 1 are the velocities of the contact point between the oscillator and the casing before and after the collision.

Figure BDA0001714804090000057
Figure BDA0001714804090000057

式中，

Figure BDA0001714804090000058
分别为碰撞前后振荡器在x1z1平面内的角速度。代入式(2)有In the formula,
Figure BDA0001714804090000058
are the angular velocities of the oscillator in the x 1 z 1 plane before and after the collision. Substituting into equation (2), we have

Figure BDA0001714804090000059
Figure BDA0001714804090000059

对于振荡器与套管的碰撞恢复系数可取钢对钢4的k＝0.56。The coefficient of recovery for the collision between the oscillator and the casing can be taken as k = 0.56 for steel to steel 4 .

根据冲量矩定理，有According to the impulse moment theorem, we have

Figure BDA00017148040900000510
Figure BDA00017148040900000510

式中，I为套管作用于振荡器的冲量，JO为振荡器系统对O轴的转动惯量。Where I is the impulse of the casing acting on the oscillator, and J O is the moment of inertia of the oscillator system about the O-axis.

由式(3)、(4)解得From equations (3) and (4), we can get

Figure BDA0001714804090000061
Figure BDA0001714804090000061

由

Figure BDA0001714804090000062
或
Figure BDA0001714804090000063
与式(1)解得初始到第一次撞击套管经历的时间t1。显然这是一个超越方程，采用试算法来求解。第一次撞击套管时的位移与速度分别为Depend on
Figure BDA0001714804090000062
or
Figure BDA0001714804090000063
The time t 1 from the initial impact to the first impact on the casing can be obtained by solving equation (1). Obviously, this is a transcendental equation, and a trial and error method is used to solve it. The displacement and velocity when the casing is first impacted are

Figure BDA0001714804090000064
Figure BDA0001714804090000064

由式(5)、式(6)解得第一次碰撞后角速度

Figure BDA0001714804090000065
和碰撞冲量I，记为
Figure BDA0001714804090000066
I1。振荡器受到碰撞后，将以
Figure BDA0001714804090000067
为初始条件，运动方程为The angular velocity after the first collision is obtained by solving equations (5) and (6):
Figure BDA0001714804090000065
and the collision impulse I, denoted as
Figure BDA0001714804090000066
I 1. After the oscillator is hit, it will
Figure BDA0001714804090000067
is the initial condition, and the equation of motion is

Figure BDA0001714804090000068
Figure BDA0001714804090000068

由

Figure BDA0001714804090000069
或
Figure BDA00017148040900000610
与式(7)试算法解得初始到第二次撞击套管经历的时间刻t2，第二次撞击套管时的角位移与角速度分别为Depend on
Figure BDA0001714804090000069
or
Figure BDA00017148040900000610
The time t 2 from the initial impact to the second impact on the casing is obtained by trial calculation with equation (7). The angular displacement and angular velocity at the second impact on the casing are

Figure BDA00017148040900000611
Figure BDA00017148040900000611

由式(5)、式(8)解得第二次碰撞后角速度

Figure BDA00017148040900000612
和碰撞冲量I，记为
Figure BDA00017148040900000613
I2。振荡器受到第二次碰撞后，将以
Figure BDA00017148040900000614
为初始条件，运动方程为The angular velocity after the second collision is obtained by solving equations (5) and (8):
Figure BDA00017148040900000612
and the collision impulse I, denoted as
Figure BDA00017148040900000613
I 2. After the oscillator is hit for the second time, it will
Figure BDA00017148040900000614
is the initial condition, and the equation of motion is

Figure BDA00017148040900000615
Figure BDA00017148040900000615

以此类推。在获得第i-1次碰撞后的ti-1,

Figure BDA00017148040900000616
Ii-1后，以
Figure BDA00017148040900000617
为初始条件，运动方程为And so on. After obtaining the i-1th collision, t i-1 ,
Figure BDA00017148040900000616
After I i-1 ,
Figure BDA00017148040900000617
is the initial condition, and the equation of motion is

Figure BDA0001714804090000071
Figure BDA0001714804090000071

由

Figure BDA0001714804090000072
或
Figure BDA0001714804090000073
与式(10)试算法解得初始到第i次撞击套管经历的时间刻ti，第i次撞击套管时的角位移和角速度分别为Depend on
Figure BDA0001714804090000072
or
Figure BDA0001714804090000073
The time from the initial impact to the ith impact on the casing is obtained by trial calculation with equation (10) as t i . The angular displacement and angular velocity at the ith impact on the casing are

Figure BDA0001714804090000074
Figure BDA0001714804090000074

由式(5)、式(11)解得第i次碰撞后角速度

Figure BDA0001714804090000075
和碰撞冲量I，记为
Figure BDA0001714804090000076
Ii。振荡器受到碰撞后，将以
Figure BDA0001714804090000077
为初始条件，运动方程为The angular velocity after the i-th collision is obtained by solving equations (5) and (11):
Figure BDA0001714804090000075
and the collision impulse I, denoted as
Figure BDA0001714804090000076
I i . After the oscillator is hit, it will
Figure BDA0001714804090000077
is the initial condition, and the equation of motion is

Figure BDA0001714804090000078
Figure BDA0001714804090000078

............

由此，确定套管中振荡器的运动行为和对套管的作用状况。该边界限定下的振荡器振动问题的解决方法与步骤如下：Thus, the motion behavior of the oscillator in the casing and the effect on the casing are determined. The solution and steps to the oscillator vibration problem under this boundary limitation are as follows:

(1)从振荡器启动开始，运动方程为式(1)，当

Figure BDA0001714804090000079
或
Figure BDA00017148040900000710
时(正负取决于式(1)此时的计算结果)，由式(1)试算出与套管第一次碰撞时间t1，由式(6)、式(5)解得与套管第一次碰撞后角速度
Figure BDA00017148040900000711
和碰撞冲量I，记为
Figure BDA00017148040900000712
I1，碰撞时角位移为
Figure BDA00017148040900000713
或
Figure BDA00017148040900000714
(1) Starting from the start of the oscillator, the motion equation is (1), when
Figure BDA0001714804090000079
or
Figure BDA00017148040900000710
When (the positive or negative value depends on the calculation result of formula (1) at this time), the first collision time t1 with the casing is calculated by formula (1), and the angular velocity after the first collision with the casing is obtained by solving formula (6) and formula (5):
Figure BDA00017148040900000711
and the collision impulse I, denoted as
Figure BDA00017148040900000712
I 1 , the angular displacement during collision is
Figure BDA00017148040900000713
or
Figure BDA00017148040900000714

(2)以

Figure BDA00017148040900000715
为初始条件，振荡器与套管第一次碰撞后的运动方程为式(7)。当
Figure BDA00017148040900000716
或
Figure BDA00017148040900000717
时(正负取决于式(7)此时的计算结果)，由式(7)试算出与套管第二次碰撞时间t2，由式(8)、式(5)解得与套管第二次碰撞后角速度
Figure BDA00017148040900000718
和碰撞冲量I，记为
Figure BDA00017148040900000719
I2，碰撞时角位移为
Figure BDA00017148040900000720
或
Figure BDA00017148040900000721
(2)
Figure BDA00017148040900000715
As the initial condition, the motion equation after the first collision between the oscillator and the casing is equation (7).
Figure BDA00017148040900000716
or
Figure BDA00017148040900000717
When (the positive or negative value depends on the calculation result of formula (7) at this time), the second collision time t2 with the casing is calculated by formula (7), and the angular velocity after the second collision with the casing is obtained by solving formula (8) and formula (5):
Figure BDA00017148040900000718
and the collision impulse I, denoted as
Figure BDA00017148040900000719
I 2 , the angular displacement during collision is
Figure BDA00017148040900000720
or
Figure BDA00017148040900000721

(3)以此类推。在获得第i-1次碰撞后的ti-1,

Figure BDA00017148040900000722
Ii-1后，以
Figure BDA0001714804090000081
为初始条件，振荡器与套管第i-1次碰撞后的运动方程为式(10)，由
Figure BDA0001714804090000082
或
Figure BDA0001714804090000083
(正负取决于式(10)此时的计算结果)与式(10)试算法解得初始到第i次撞击套管经历的时间刻ti。碰撞时角位移为
Figure BDA0001714804090000084
或
Figure BDA0001714804090000085
由式(11)、式(5)解得与套管第i次碰撞后角速度
Figure BDA0001714804090000086
和碰撞冲量I，记为
Figure BDA0001714804090000087
Ii。(3) And so on. After obtaining the i-1th collision t i-1 ,
Figure BDA00017148040900000722
After I i-1 ,
Figure BDA0001714804090000081
As the initial condition, the motion equation after the oscillator and the casing collide for the i-1th time is (10), which is given by
Figure BDA0001714804090000082
or
Figure BDA0001714804090000083
(The positive or negative value depends on the calculation result of formula (10) at this time) and formula (10) are used to solve the time t i from the initial to the i-th impact on the casing. The angular displacement at the time of collision is
Figure BDA0001714804090000084
or
Figure BDA0001714804090000085
The angular velocity after the i-th collision with the casing is obtained by solving equations (11) and (5):
Figure BDA0001714804090000086
and the collision impulse I, denoted as
Figure BDA0001714804090000087
I i .

如此最终获得一系列振荡器对套管的作用时间与碰撞冲量ti、Ii；据此评估振荡器对套管的作用情况，如撞击强度和频率(通过ti确定各相邻碰撞间隔时间，然后平均统计出碰撞周期、频率)。In this way, a series of oscillator action time and collision impulse ti , Ii on the casing are finally obtained; based on this, the action of the oscillator on the casing, such as the impact intensity and frequency, is evaluated (the interval between adjacent collisions is determined by ti , and then the collision cycle and frequency are averaged and counted).

本发明根据动力学和振动力学理论，针对振荡器在直井套管中的运动和对套管的作用行为，进行模拟分析，确定了分析振荡器对套管水泥固实效果的评估方案，建立了在偏心转子激励下振荡器在直井套管中的反映主要运动特征的运动微分方程并确定其运动规律，然后试算确定由于套管对振荡器的运动限制产生的非线性边界问题，并结合碰撞理论，评估振荡器对套管的作用规律，最后据此分析由振荡器引起的套管振动行为并评估振荡器对套管水泥固实效果。为探索评估振荡器对套管水泥固实效果奠定理论基础。According to the theory of dynamics and vibration mechanics, the present invention simulates and analyzes the movement of the oscillator in the vertical well casing and its action on the casing, determines an evaluation scheme for analyzing the effect of the oscillator on the cement consolidation of the casing, establishes a motion differential equation reflecting the main motion characteristics of the oscillator in the vertical well casing under the excitation of the eccentric rotor and determines its motion law, then calculates and determines the nonlinear boundary problem caused by the motion restriction of the oscillator by the casing, and evaluates the action law of the oscillator on the casing in combination with the collision theory, and finally analyzes the vibration behavior of the casing caused by the oscillator and evaluates the cement consolidation effect of the oscillator on the casing. This lays a theoretical foundation for exploring and evaluating the cement consolidation effect of the oscillator on the casing.

以上所述仅是对本发明的较佳实施方式而已，并非对本发明作任何形式上的限制，凡是依据本发明的技术实质对以上实施方式所做的任何简单修改，等同变化与修饰，均属于本发明技术方案的范围内。The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are within the scope of the technical solution of the present invention.

Claims (1)

1. The method for analyzing and evaluating the motion of the oscillator in the casing slurry and the action of the oscillator on the casing is characterized by comprising the following steps of:
(1) Starting from the start of the oscillator, the equation of motion is as shown in equation (1) when
Figure FDA0001714804080000011
Or->
Figure FDA0001714804080000012
Then, the first time collision time t with the casing is calculated by the formula (1) 1 The clearance speed after the first collision with the sleeve is obtained by solving the formula (6) and the formula (5)>
Figure FDA0001714804080000013
And impact of collision I, recorded as
Figure FDA0001714804080000014
I 1 Angular displacement of ^ 5 upon collision>
Figure FDA0001714804080000015
Or>
Figure FDA0001714804080000016
(2) To be provided with
Figure FDA0001714804080000017
For the initial condition, the equation of motion after the first impact of the oscillator with the casing is equation (7) when
Figure FDA0001714804080000018
Or->
Figure FDA0001714804080000019
Calculating the second collision time t with the casing according to the equation (7) 2 The rear angle speed after the second collision with the sleeve is obtained by solving the formula (8) and the formula (5)>
Figure FDA00017148040800000110
And a collision impulse I, recorded as>
Figure FDA00017148040800000111
I 2 Angular displacement of ^ 5 upon collision>
Figure FDA00017148040800000112
Or->
Figure FDA00017148040800000113
(3) By analogy, t after the i-1 st collision is obtained i-1 ,
Figure FDA00017148040800000114
I i-1 Then, in
Figure FDA00017148040800000115
For the initial condition, the equation of motion after the i-1 st collision of the oscillator with the housing is given by (10)>
Figure FDA00017148040800000116
Or->
Figure FDA00017148040800000117
Solving with the formula (10) to obtain the time t of the ith impacting casing i Angular displacement of ^ 5 upon collision>
Figure FDA00017148040800000118
Or->
Figure FDA00017148040800000119
The clearance speed after the ith collision with the sleeve is obtained by solving the formula (11) and the formula (5)>
Figure FDA00017148040800000120
And impact of collision I, recorded as
Figure FDA00017148040800000121
I i ；
Finally obtaining the action time and the collision impulse t of a series of oscillators to the sleeve i 、I i (ii) a Evaluating the action condition of the oscillator on the sleeve according to the above;
wherein the movement of the oscillator in the sleeve is limited by the sleeve, when the transverse displacement reaches the difference between the outer radius of the oscillator and the inner radius of the sleeve, the oscillator collides with the sleeve, and the inner diameter of the sleeve is set as D 1 When the oscillator collides with the sleeve, the oscillator reaches the maximum angular displacement of
Figure FDA00017148040800000122
In the formula (I), the compound is shown in the specification,
Figure FDA00017148040800000123
is the angle between the axis of the oscillator and the z-axis, D 1 Is the inner diameter of the sleeve, l is the length of the oscillator, D is the outer diameter of the outer cylinder of the oscillator, l 1 The distance between the top of the oscillator and the suspension point O is defined, and alpha is an included angle between the centroid of the bottom of the oscillator and a connecting line between a contact point of the oscillator and the sleeve and the suspension point O respectively;
before the oscillator starts, the oscillator is at rest and at an angular positionMoving device
Figure FDA00017148040800000124
Angular velocity->
Figure FDA00017148040800000125
I.e. an initial condition of->
Figure FDA0001714804080000021
The motion equation of the oscillator is
Figure FDA0001714804080000022
Where ξ is the damping ratio of the oscillator system, p is the natural frequency of the oscillator system,
Figure FDA0001714804080000023
is the natural frequency of the oscillator, ω is the angular speed of rotation of the oscillator rotor, α 0 Is the initial phase of the steady state response of the oscillator system, phi is the amplitude of the steady state response of the oscillator system;
the coefficient of restitution of the collision between the oscillator and the sleeve is set as k,
Figure FDA0001714804080000024
in the formula, v 1 、u 1 The velocities of the oscillator and the casing contact point before and after the collision, respectively
Figure FDA0001714804080000025
In the formula (I), the compound is shown in the specification,
Figure FDA0001714804080000026
oscillator in x before and after collision respectively 1 z 1 Angular velocity in plane, instead ofFormula (2) is
Figure FDA0001714804080000027
For the collision recovery coefficient k =0.56 of the oscillator with the bushing,
according to the impulse moment theorem, there are
Figure FDA0001714804080000028
Wherein I is the impulse of the sleeve acting on the oscillator, J O The moment of inertia of the oscillator system to the O-axis,
is obtained by the resolution of the formulas (3) and (4)
Figure FDA0001714804080000029
By
Figure FDA00017148040800000210
Or->
Figure FDA00017148040800000211
And (2) solving by adopting a trial algorithm to obtain the time t for initially impacting the casing for the first time 1 The angular displacement and the angular velocity are respectively when the casing pipe is impacted for the first time
Figure FDA00017148040800000212
The angular velocity after the first collision is obtained by solving the equations (5) and (6)
Figure FDA00017148040800000213
And a collision impulse I, recorded as>
Figure FDA00017148040800000214
I 1 After the oscillator is collided, the signal is judged to be greater or less than>
Figure FDA0001714804080000031
For the initial condition, the equation of motion is
Figure FDA0001714804080000032
By
Figure FDA0001714804080000033
Or>
Figure FDA0001714804080000034
Solving with the formula (7) to obtain the time t for the second impact on the casing 2 The angular displacement and the angular velocity are respectively equal to
Figure FDA0001714804080000035
The angular velocity after the second collision is obtained by solving the equations (5) and (8)
Figure FDA0001714804080000036
And a collision impulse I, recorded as>
Figure FDA0001714804080000037
I 2 After the oscillator is subjected to the second collision, will be based on->
Figure FDA0001714804080000038
For the initial condition, the equation of motion is
Figure FDA0001714804080000039
By analogy, t after the i-1 st collision is obtained i-1 ,
Figure FDA00017148040800000310
I i-1 Then, in order
Figure FDA00017148040800000311
For the initial condition, the equation of motion is
Figure FDA00017148040800000312
By
Figure FDA00017148040800000313
Or->
Figure FDA00017148040800000314
Solving with the formula (10) to obtain the time t of the ith impacting casing i The angular displacement and the angular velocity of the ith impact on the sleeve are respectively
Figure FDA00017148040800000315
The i-th collision relief angle velocity is obtained by solving the equations (5) and (11)
Figure FDA00017148040800000316
And a collision impulse I, marked>
Figure FDA00017148040800000317
I i After the oscillator is collided, the signal is judged to be greater or less than>
Figure FDA0001714804080000041
As an initial condition, the equation of motion is
Figure FDA0001714804080000042
From this, the motion behaviour of the oscillator in the casing and the action situation on the casing are determined.
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