CN108984872A - The movement of oscillator and its analyzing evaluation method to casing effect in casing mud - Google Patents
The movement of oscillator and its analyzing evaluation method to casing effect in casing mud Download PDFInfo
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- CN108984872A CN108984872A CN201810702491.2A CN201810702491A CN108984872A CN 108984872 A CN108984872 A CN 108984872A CN 201810702491 A CN201810702491 A CN 201810702491A CN 108984872 A CN108984872 A CN 108984872A
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Abstract
The main movement behavior of oscillator and its analyzing evaluation method to casing effect in casing mud of the present invention calculate record time of origin t by the equation of motion since oscillator starting1, solveThe movement of oscillator is that oscillator movement is superimposed with the residual vibration that casing collision generates before colliding, whenOrWhen, by moving equation calculation record time of origin t at this time2, solveWithOrFor primary condition, it is superimposed with the residual vibration that casing collision generates in the equation of motion, so analogically, solves time, first angular speed and the impact pulse t of each casing collisioni、So a series of oscillators are finally obtained to casingOrAction time and impact pulse ti、Ii；The beneficial effects of the invention are as follows can effectively analyze in assessment casing mud the main movement behavior of oscillator and its provide data support to the effect of cement slurry to the effect of casing and for analysis casing.
Description
Technical field
The invention belongs to drilling technology field, it is related to the movement of oscillator and its function analysis to casing in casing mud
Appraisal procedure.
Background technique
During drilling completion, the quality of the solid casing of cement injection will directly affect the as received basis of complete well rear sleeve
Amount.If cementing concrete is unevenly distributed leakiness, it will result in sleeve stress and be unevenly prone to breakage.Therefore, it is perfused
How cement reaches uniformly densely effect, is always well completion work person's concern.For this purpose, people devise different vibrations
It swings in device tripping in casing, evoking set tube vibration to scheme to impact casing by the swing of oscillator promotes cement wave outside casing
It is dynamic, reach cementing concrete and is evenly distributed dense effect.But theory analysis verifying support is lacked to this, data is rare.Attempt herein
By carrying out sunykatuib analysis, Exploring Analysis vibration to movement of the oscillator in straight well casing and to the main behavior of the effect of casing
Device is swung to the evaluation scheme of the solid effect of casing cement.
Summary of the invention
The purpose of the present invention is to provide the movement of oscillator in casing mud and its to the analysis assessment side of casing effect
Method, the beneficial effects of the invention are as follows the main movement behavior that can determine oscillator in casing mud and its to the effect effect of casing
Fruit.
The technical scheme adopted by the invention is that following the steps below:
(1) since oscillator starting, the equation of motion is formula (1), whenOrWhen (it is positive and negative depend on formula (1)
Calculated result at this time), gone out and casing first time collision time t by formula (1) tentative calculation1, solved and casing by formula (6), formula (5)
Angular speed after primary collisionWith impact pulse I, it is denoted asI1, when collision angular displacement beOr
(2) withFor primary condition, the equation of motion after oscillator and casing collision for the first time is formula
(7).WhenOrWhen (positive and negative depend on the calculated result of formula (7) at this time), gone out by formula (7) tentative calculation and second of casing
Collision time t2, angular speed after colliding with second of casing is solved by formula (8), formula (5)With impact pulse I, it is denoted asI2,
Angular displacement is when collisionOr
(3) and so on.T after obtaining (i-1)-th collisioni-1,Ii-1Afterwards, withFor primary condition, oscillator is formula (10) with the equation of motion after casing (i-1)-th time collision,
ByOr(positive and negative to depend on the calculated result of formula (10) at this time) solves with formula (10) trial and error procedure and initially hits to i-th
The time for hitting casing experience carves ti.Angular displacement is when collisionOrIt is solved and is touched with casing i-th by formula (11), formula (5)
Hit rear angular speedWith impact pulse I, it is denoted asIi。
So finally obtain action time and impact pulse t of a series of oscillators to casingi、Ii；Oscillator is assessed accordingly
(t is passed through to the operative condition of casing, such as impact strength and frequencyiDetermine each adjacent collision interval time, then average statistics go out
Collide period, frequency).
Wherein, the movement of the oscillator in casing is limited by casing, when lateral displacement reach oscillator outer radius with
It when casing inside radius difference, will collide with casing, when colliding with casing, oscillator reaches maximum angular displacement and is
In formula, D1For casing inner diameter, l is oscillator length, and D is oscillator outer cylinder outer diameter, l1It is oscillator top from suspension point
The distance of O, α be oscillator bottom centroid and with the cannula contact angle between the line of suspension point O respectively.
Before oscillator starts, oscillator is static, angular displacementAngular speedI.e. primary condition is
The oscillator equation of motion is
In formula, ξ is the damping ratio of oscilator system, and p is the intrinsic frequency of oscilator system,For oscillator
Decaying intrinsic frequency, ω be oscillator rotor rotational angular velocity, α0For oscilator system steady-state response initial phase, Φ is oscillation
Device systematic steady state response amplitude.
If oscillator and casing collide, recovery coefficient is k, then
In formula, v1、u1The respectively speed of collision front and back oscillator and cannula contact, then
In formula,Respectively collision front and back oscillator is in x1z1Angular speed in plane, substituting into formula (2) has
For being all that the oscillator of steel and the collision recovery coefficient of casing can detect k=0.56.
According to momentum theorem of moments, have
In formula, I is the momentum that casing acts on oscillator, JOIt is oscilator system to the rotary inertia of O axis.
It is solved by formula (3), (4)
ByOrThe initial time t to shock casing experience for the first time is solved using trial and error procedure with formula (1)1, the
Primary angular displacement when hitting casing is respectively with angular speed
Angular speed after colliding for the first time is solved by formula (5), formula (6)With impact pulse I, it is denoted asI1.Oscillator by
It, will be with to after collisionFor primary condition, the equation of motion is
ByOrThe time for solving initial to second shock casing experience with formula (7) trial and error procedure carves t2, the
Angular displacement when secondary impact casing is respectively with angular speed
Angular speed after second of collision is solved by formula (5), formula (8)With impact pulse I, it is denoted asI2.Oscillator by
It, will be with after being collided to secondFor primary condition, the equation of motion is
And so on.T after obtaining (i-1)-th collisioni-1,Ii-1Afterwards, withFor primary condition, the equation of motion is
ByOrThe initial quarter time t that casing experience is hit to i-th is solved with formula (10) trial and error procedurei, i-th
Angular displacement and angular speed when secondary shock casing are respectively
Angular speed after i-th is collided is solved by formula (5), formula (11)With impact pulse I, it is denoted asIi.Oscillator by
It, will be with to after collisionFor primary condition, the equation of motion is
The motor behavior of oscillator and the effect situation to casing in casing are determined as a result,.
Detailed description of the invention
Fig. 1 is to shake to swash device and casing-contact collision schematic diagram.
Specific embodiment
The present invention is described in detail With reference to embodiment.
The movement of oscillator in casing is limited by casing, when lateral displacement reaches in oscillator outer radius and casing
When semidiameter (abbreviation apparent radius), it will collide with casing.Belong to boundary nonlinear vibration problem.If casing inner diameter is
D1, when oscillator and casing collide, as shown in Figure 1.
Before oscillator starts,I.e.
In formula, ξ is the damping ratio of oscilator system, and p is the intrinsic frequency of oscilator system,For oscillator
Decaying intrinsic frequency, ω be oscillator rotor rotational angular velocity, α0For oscilator system steady-state response initial phase, Φ is oscillation
Device systematic steady state response amplitude.
If oscillator and casing collide, recovery coefficient is k.Consider the lateral velocity of rum point on the casing of collision front and back
Much smaller compared with the lateral velocity of oscillator rum point, by collision theory, approximation has
In formula, v1、u1The respectively speed of collision front and back oscillator and cannula contact.Then
In formula,Respectively collision front and back oscillator is in x1z1Angular speed in plane.Substitution formula (2) has
Steel to steel can use for the collision recovery coefficient of oscillator and casing4K=0.56.
According to momentum theorem of moments, have
In formula, I is the momentum that casing acts on oscillator, JOIt is oscilator system to the rotary inertia of O axis.
It is solved by formula (3), (4)
ByOrIt is solved with formula (1) initial to the time t for hitting casing experience for the first time1.Obviously this is one
Transcendental equation is solved using trial and error procedure.For the first time hit casing when displacement be respectively with speed
Angular speed after colliding for the first time is solved by formula (5), formula (6)With impact pulse I, it is denoted asI1.Oscillator by
It, will be with to after collisionFor primary condition, the equation of motion is
ByOrThe time for solving initial to second shock casing experience with formula (7) trial and error procedure carves t2, second
It is secondary hit casing when angular displacement be respectively with angular speed
Angular speed after second of collision is solved by formula (5), formula (8)With impact pulse I, it is denoted asI2.Oscillator by
It, will be with after being collided to secondFor primary condition, the equation of motion is
And so on.T after obtaining (i-1)-th collisioni-1,Ii-1Afterwards, withFor primary condition, the equation of motion is
ByOrThe initial quarter time t that casing experience is hit to i-th is solved with formula (10) trial and error procedurei, i-th
Angular displacement and angular speed when secondary shock casing are respectively
Angular speed after i-th is collided is solved by formula (5), formula (11)With impact pulse I, it is denoted asIi.Oscillator by
It, will be with to after collisionFor primary condition, the equation of motion is
......
The motor behavior of oscillator and the effect situation to casing in casing are determined as a result,.Oscillation under the borders
The solution of device vibration problem with steps are as follows:
(1) since oscillator starting, the equation of motion is formula (1), whenOrWhen (it is positive and negative depend on formula (1) this
When calculated result), by formula (1) tentative calculation go out and casing first time collision time t1, solved and casing first by formula (6), formula (5)
Angular speed after secondary collisionWith impact pulse I, it is denoted asI1, when collision angular displacement beOr
(2) withFor primary condition, the equation of motion after oscillator and casing collision for the first time is formula
(7).WhenOrWhen (positive and negative depend on the calculated result of formula (7) at this time), gone out by formula (7) tentative calculation and second of casing
Collision time t2, angular speed after colliding with second of casing is solved by formula (8), formula (5)With impact pulse I, it is denoted as
I2, when collision angular displacement beOr
(3) and so on.T after obtaining (i-1)-th collisioni-1,Ii-1Afterwards, withFor primary condition, oscillator is formula (10) with the equation of motion after casing (i-1)-th time collision,
ByOr(positive and negative to depend on the calculated result of formula (10) at this time) solves with formula (10) trial and error procedure and initially hits to i-th
The time for hitting casing experience carves ti.Angular displacement is when collisionOrIt is solved and is touched with casing i-th by formula (11), formula (5)
Hit rear angular speedWith impact pulse I, it is denoted asIi。
So finally obtain action time and impact pulse t of a series of oscillators to casingi、Ii；Oscillator is assessed accordingly
(t is passed through to the operative condition of casing, such as impact strength and frequencyiDetermine each adjacent collision interval time, then average statistics go out
Collide period, frequency).
The present invention is theoretical according to dynamics and vibration mechanics, for movement of the oscillator in straight well casing and to casing
Function carries out sunykatuib analysis, it is determined that analysis oscillator establishes inclined the evaluation scheme of the solid effect of casing cement
The differential equation of motion of reflection main movement feature of the oscillator in straight well casing and its determining movement rule under heart rotor excitation
Rule, then tentative calculation determines the nonlinear boundary problem generated due to casing to the movement limitation of oscillator, and combines collision theory,
Oscillator is assessed to the action rule of casing, finally analyze the set tube vibration behavior as caused by oscillator accordingly and assesses oscillator
To the solid effect of casing cement.To explore assessment oscillator to the solid effect based theoretical of casing cement.
The above is only not to make limit in any form to the present invention to better embodiment of the invention
System, any simple modification that embodiment of above is made according to the technical essence of the invention, equivalent variations and modification,
Belong in the range of technical solution of the present invention.
Claims (1)
1. the movement of oscillator and its analyzing evaluation method to casing effect in casing mud, it is characterised in that according to following step
It is rapid to carry out:
(1) since oscillator starting, the equation of motion is formula (1), whenOrWhen, gone out and casing the by formula (1) tentative calculation
Primary collision time t1, angular speed after colliding for the first time with casing is solved by formula (6), formula (5)With impact pulse I, it is denoted asI1, when collision angular displacement beOr
(2) withFor primary condition, the equation of motion after oscillator and casing collision for the first time is formula (7), whenOrWhen by formula (7) tentative calculation go out and second of collision time t of casing2, solved and casing second by formula (8), formula (5)
Angular speed after secondary collisionWith impact pulse I, it is denoted asI2, when collision angular displacement beOr
(3) and so on, the t after obtaining (i-1)-th collisioni-1,Ii-1Afterwards, withFor primary condition, oscillator is formula (10) with the equation of motion after casing (i-1)-th time collision,
ByOrThe initial quarter time t that casing experience is hit to i-th is solved with formula (10) trial and error procedurei, angular displacement when collision
ForOrIt is solved and angular speed after the collision of casing i-th by formula (11), formula (5)With impact pulse I, it is denoted as
Ii；
So finally obtain action time and impact pulse t of a series of oscillators to casingi、Ii；Assessment oscillator is to set accordingly
The operative condition of pipe；
Wherein, the movement of the oscillator in casing is limited by casing, when lateral displacement reaches oscillator outer radius and casing
It when inside radius difference, will collide with casing, if casing inner diameter is D1, when oscillator and casing collide, oscillator reaches
It is to maximum angular displacement
In formula,For the angle of oscillator axis and z-axis, D1For casing inner diameter, l is oscillator length, and D is outside oscillator outer cylinder
Diameter, l1Be at the top of oscillator with a distance from suspension point O, α be oscillator bottom centroid and with the cannula contact company with suspension point O respectively
Angle between line；
Before oscillator starts, oscillator is static, angular displacementAngular speedI.e. primary condition isOscillation
The device equation of motion is
In formula, ξ is the damping ratio of oscilator system, and p is the intrinsic frequency of oscilator system,For declining for oscillator
Subtract intrinsic frequency, ω is oscillator rotor rotational angular velocity, α0For oscilator system steady-state response initial phase, Φ is oscillator system
System steady-state response amplitude；
If oscillator and casing collide, recovery coefficient is k,
In formula, v1、u1The respectively speed of collision front and back oscillator and cannula contact, then
In formula,Respectively collision front and back oscillator is in x1z1Angular speed in plane, substituting into formula (2) has
For the collision recovery coefficient k=0.56 of oscillator and casing,
According to momentum theorem of moments, have
In formula, I is the momentum that casing acts on oscillator, JOIt is oscilator system to the rotary inertia of O axis,
It is solved by formula (3), (4)
ByOrThe initial time t to shock casing experience for the first time is solved using trial and error procedure with formula (1)1, for the first time
Hit casing when angular displacement be respectively with angular speed
Angular speed after colliding for the first time is solved by formula (5), formula (6)With impact pulse I, it is denoted asI1, oscillator is collided
It afterwards, will be withFor primary condition, the equation of motion is
ByOrThe time for solving initial to second shock casing experience with formula (7) trial and error procedure carves t2, hit for the second time
Angular displacement when hitting casing is respectively with angular speed
Angular speed after second of collision is solved by formula (5), formula (8)With impact pulse I, it is denoted asI2, oscillator is by second
It, will be with after secondary collisionFor primary condition, the equation of motion is
And so on, the t after obtaining (i-1)-th collisioni-1,Ii-1Afterwards, withFor primary condition, the equation of motion is
ByOrThe initial quarter time t that casing experience is hit to i-th is solved with formula (10) trial and error procedurei, i-th hits
Angular displacement and angular speed when hitting casing are respectively
Angular speed after i-th is collided is solved by formula (5), formula (11)With impact pulse I, it is denoted asIi, oscillator touched
It, will be with after hittingFor primary condition, the equation of motion is
The motor behavior of oscillator and the effect situation to casing in casing are determined as a result,.
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2018
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| JP2004054836A (en) * | 2002-07-24 | 2004-02-19 | Ebara Corp | Wall surface impact simulation method for solid-liquid mixed-phase fluid |
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| CN101558174A (en) * | 2005-09-23 | 2009-10-14 | Uit有限责任公司 | Method of metal performance improvement and protection against degradation and suppression thereof by ultrasonic impact |
| CN103383298A (en) * | 2013-07-11 | 2013-11-06 | 冯辅周 | Method for analyzing vibration characteristics of solid slab under ultrasonic excitation |
| CN104747119A (en) * | 2013-12-31 | 2015-07-01 | 中国石油化工集团公司 | Vibration well cementation device and vibration well cementation method |
| CN105525892A (en) * | 2014-09-28 | 2016-04-27 | 中国石油化工集团公司 | Casing pipe vibrating device |
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