CN110344819A - A kind of high temperature and pressure high gas rate well completion tubular column vibration prediction method - Google Patents
A kind of high temperature and pressure high gas rate well completion tubular column vibration prediction method Download PDFInfo
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- CN110344819A CN110344819A CN201910697668.9A CN201910697668A CN110344819A CN 110344819 A CN110344819 A CN 110344819A CN 201910697668 A CN201910697668 A CN 201910697668A CN 110344819 A CN110344819 A CN 110344819A
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B47/00—Survey of boreholes or wells
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B47/00—Survey of boreholes or wells
- E21B47/007—Measuring stresses in a pipe string or casing
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Abstract
The invention belongs to oil-gas mining technical fields, specifically, it is related to a kind of high temperature and pressure high gas rate well completion tubular column vibration prediction method, the following steps are included: A, horizontally to the right for x-axis, well vertical depth direction is y-axis, the longitudinal and lateral coupling kinetic model for establishing tubing string obtains tubing string total kinetic energy T, total potential energy U calculating formula；B, according to Hamiton's principle, derive that the calculating formula difference of tubing string extensional vibration differential equation f (x, t) and tubing string oscillation crosswise differential equation p (x, t) is as follows by tubing string total kinetic energy T, total potential energy U calculating formula；C, the longitudinally, laterally oscillatory differential equation of tubing string is solved；D, vertical, horizontal vibration displacement, tubing string axial stress, tubing string payload and the tubing string moment of flexure of calculated result analysis tubing string are utilized.High temperature and pressure high gas rate well completion tubular column vibration prediction method provided by the invention can get the stress condition of any element length tubing string in completion tubular column, can design high temperature and pressure high-yield well completion tubular column, construction, safeguard that aspect provides theory support.
Description
Technical field
The invention belongs to oil-gas mining technical fields, in particular to a kind of high temperature and pressure high gas rate well completion tubular column
Vibration prediction method.
Background technique
High temperature and pressure high-yield well is often referred to well head pressure greater than 70MPa (or bottom pressure is greater than 105MPa), bottom hole temperature (BHT)
Higher than the well that 150 DEG C, yield are greater than 120 × 104m3/d.High temperature and pressure high-yield well has the feature that compared with conventional gas well
High temperature can heat annular space completion fluid, and annular pressure is caused passively to increase, and passive raised annular pressure is easy to cause casing collapse；
On the one hand high pressure makes casing occur to squeeze the increased risk ruined, on the other hand, will lead to big, the excessive well depth of well head switch well pressure
The stress that will lead to completion tubular column and deformation are to the coulomb between temperature, pressure, fluid density, viscous frictional resistance, oil pipe and the borehole wall
The sensibility of the factors such as frictional force increases, i.e., deformation caused by the temperature effect, ballooning effect of tubing string and piston effect is to tubing string
The influence of job security is prominent；High yield fluid easily causes the low-frequency vibration, the aperiodicity high vibration that are bent tubing string, aggravation mill
Damage, leads to tubing string premature failure, is forced underground work, even result in pit shaft and scrap, it is complete to thereby result in high temperature and pressure high-yield well
Well operations difficulty is big, risk is high.Therefore scene needs to carry out the vibration characteristics experimental study of high temperature and pressure high-yield well completion tubular column,
Completion tubular column stress condition is analyzed, provides effective technology guarantor for the design, construction, maintenance of high temperature and pressure high-yield well completion tubular column
Barrier.
Summary of the invention
To solve drawbacks described above of the existing technology, the present invention provides a kind of high temperature and pressure high gas rate well completion tubular columns
Vibration prediction method.
Technical scheme is as follows:
The present invention provides a kind of high temperature and pressure high gas rate well completion tubular column vibration prediction methods, including the following steps:
A, with horizontally to the right for x-axis, well vertical depth direction is y-axis, the longitudinal and lateral coupling kinetic model of tubing string is established, pipe is obtained
Column total kinetic energy T, total potential energy U calculating formula difference are as follows:
In formula: L is tubing string length (m)；ρ is tubing string density (kg/m3)；A is tubing string cross-sectional area (m2)；U is vertical for tubing string
To displacement (m)；W is tubing string lateral displacement (m)；V is tube fluid speed (m/s)；ρoFor fluid density (kg/m in tubing string3)；E
For tubing string elasticity modulus (MPa)；EI is drilling pipe bending rigidity (Nm2)；T is the time (s)；
B, according to Hamiton's principle, derive that tubing string extensional vibration is micro- by above-mentioned tubing string total kinetic energy T, total potential energy U calculating formula
Divide the calculating formula of Equation f (x, t) and tubing string oscillation crosswise differential equation p (x, t) difference as follows:
C, the longitudinally, laterally oscillatory differential equation of tubing string is solved, and exports calculated result with computer；
D, the vertical, horizontal vibration displacement of above-mentioned calculated result analysis tubing string, tubing string axial stress, tubing string payload are utilized
With tubing string moment of flexure.
It is further comprising the steps of in above-mentioned steps C in the embodiment that invention provides:
1), using linear Lagrangian and hermite function three times, by the length travel u and lateral displacement of tubing string
Field w carries out finite element discretization；
2) the finite element discretization form of the length travel u of tubing string and lateral displacement field w, are substituted into tubing string in above-mentioned steps A
The tubing string total kinetic energy T indicated with displacement of joint vector, the canonical form of total potential energy U are obtained in total kinetic energy T, total potential energy U calculating formula,
Its expression formula difference is as follows:
3), the displacement of joint vector form based on above-mentioned tubing string total kinetic energy T, total potential energy U, further according to variation principle, in conjunction with
Tubing string extensional vibration differential equation f (x, t) and tubing string oscillation crosswise differential equation p (x, t), obtains the dynamics of tubing string discrete form
Equation is as follows:
4), by the coordinate transformation of tubing string in lower curved section to horizontally to the right for x-axis, well vertical depth direction is the entirety in y-axis
In coordinate system；
5), using the method for solving of Newmark- β step_by_step integration, utilize computer programming, solve above-mentioned steps 3) in pipe
The kinetics equation of column discrete form, and export calculated result.
The utility model has the advantages that high temperature and pressure high gas rate well completion tubular column vibration prediction method provided by the invention can pass through computer
Programming carries out operation, it is easy to operate, calculate quickly, by this method can get any element length tubing string in completion tubular column by
Power situation, through practical proof, this method computational accuracy is also able to satisfy field demand, can be to high temperature and pressure high-yield well by this method
Completion tubular column design, construction, maintenance aspect provide theory support.
Detailed description of the invention
It, below will be to use required in embodiment in order to illustrate more clearly of the technical solution of embodiment of the present invention
Attached drawing be briefly described, it should be understood that the following drawings illustrates only certain embodiments of the present invention, therefore is not to be seen as
It is the restriction to range, it for those of ordinary skill in the art, without creative efforts, can be with root
Other relevant attached drawings are obtained according to these attached drawings.
Fig. 1 completion tubular column infinitesimal section force analysis figure provided by the invention；
Pipe unit schematic diagram in Fig. 2 global coordinate system provided by the invention；
Fig. 3 high temperature and pressure high gas rate well completion tubular column vibration prediction method calculation flow chart provided by the invention；
The vibration shape figure of Fig. 4 tubing string different moments provided by the invention；
The vertical, horizontal vibration displacement timeamplitude map of Fig. 5 tubing string provided by the invention；
The axial stress timeamplitude map of Fig. 6 tubing string provided by the invention；
The axle power timeamplitude map of Fig. 7 tubing string provided by the invention；
The moment of flexure timeamplitude map of Fig. 8 tubing string provided by the invention.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
To keep the purposes, technical schemes and advantages of embodiment of the present invention clearer, implement below in conjunction with the present invention
The technical solution in embodiment of the present invention is clearly and completely described in attached drawing in mode, it is clear that described reality
The mode of applying is some embodiments of the invention, rather than whole embodiments.Therefore, below to the sheet provided in the accompanying drawings
The detailed description of the embodiment of invention is not intended to limit the range of claimed invention, but is merely representative of the present invention
Selected embodiment.Based on the embodiment in the present invention, those of ordinary skill in the art are not making creative work
Under the premise of every other embodiment obtained, shall fall within the protection scope of the present invention.
The present invention provides a kind of high temperature and pressure high gas rate well completion tubular column vibration prediction methods, including the following steps:
A, prismatic fluid-transporting tubing is reduced to according to the structure of practical high temperature and pressure high gas rate well completion tubular column.Pipe
High temperature and high pressure gas inside column is the principal element for causing tubing string to vibrate, and the effect of gas makes tubing string generate vertical and horizontal vibration
It is dynamic, but vertical and horizontal vibration is not again independent split movement, it influences each other between them, therefore establish the vertically and horizontally coupling of tubing string
Kinetic model is closed, with horizontally to the right for x-axis, well vertical depth direction is y-axis, packer is reduced to fixing end, the letter of upper end tubing hanger
Fixing end is turned to, takes tubular element force analysis as shown in Figure 1.
Tubing string is reduced to uniform Rayleigh beam, if considering to couple in length and breadth, geometrical relationship are as follows:
In formula, εij(i, j=x, y, z) is 6 components of strain；It is displaced (u1,u2,u3) it is corresponding with coordinate system (x, y, z)
It is displaced field function, expression formula are as follows:
In formula, u is tubing string length travel (m)；W is tubing string lateral displacement (m)；T is the time (s)；Formula (2) are substituted into formula 1)
:
The horizontal component and vertical component of tube fluid speed V is respectively as follows:
Therefore, the total kinetic energy T of tubing string is that pipeline kinetic energy adds fluid dynamic energy, is indicated are as follows:
Total potential energy U of tubing string are as follows:
In formula (4), (5): L is tubing string length (m)；ρ is tubing string density (kg/m3)；A is tubing string cross-sectional area (m2)；U is
Tubing string length travel (m)；W is tubing string lateral displacement (m)；V is tube fluid speed (m/s)；ρoFor fluid density in tubing string
(kg/m3)；E is tubing string elasticity modulus (MPa)；EI is drilling pipe bending rigidity (Nm2)；T is the time (s).
B, according to Hamiton's principle, derive that tubing string extensional vibration is micro- by above-mentioned tubing string total kinetic energy T, total potential energy U calculating formula
Divide the calculating formula of Equation f (x, t) and tubing string oscillation crosswise differential equation p (x, t) difference as follows:
C, the longitudinally, laterally oscillatory differential equation of tubing string is solved, and exports calculated result with computer, further include
Following steps:
1), using linear Lagrangian and hermite function three times, by the length travel u and lateral displacement of tubing string
Field w carries out finite element discretization；
In formula:
In formula: l is the length (m) of unit.
2) displacement function formula (8), are substituted into formula (4), in (5), the available strain energy indicated with displacement of joint vector
The canonical form of function U, energetic function T:
Abbreviation obtains:
Cell matrix in formula are as follows:
Wherein:
k1And k4Strain bar unit and the three times stiffness matrix of beam element are waited to be common；k2And k3For beam element coupling in length and breadth
Close stiffness matrix, k5To flow influence in pipe, element is directly related with vibrational state, i.e., stiffness matrix is time-varying.?
When forming the two coupling matrixs, the stiffness matrix at current time is calculated using the motion vector of previous moment.
3), the displacement of joint vector form based on above-mentioned tubing string total kinetic energy T, total potential energy U, further according to variation principle, in conjunction with
Tubing string extensional vibration differential equation f (x, t) and tubing string oscillation crosswise differential equation p (x, t), obtains the dynamics of tubing string discrete form
Equation is as follows:
In formula: M, C, K and F are respectively overall quality matrix, damping matrix, stiffness matrix and the load column vector of structure.
4), the local coordinate of tubing string in lower curved section is transformed into so that horizontally to the right for x-axis, well vertical depth direction is in y-axis
In global coordinate system.The pipe unit being illustrated in figure 2 in a global coordinate system, end node there are two it, the length of pipe unit are
L, elasticity modulus E, the area of cross section are A, the moment of inertia Iz。
If the modal displacement array of (Oxy) is under local coordinate system
The modal displacement array of (Oxy) is in global coordinate system
Note: rotational angle theta1And θ2It is identical in two coordinate systems.According to the motion vector equivalent in two coordinate systems
Principle, can derive following transformation relation.
Being write as matrix form has
Wherein TeFor the transformation matrix of coordinates of unit, i.e.,
It is similar with the coordinate transform of plane bar unit, stiffness equations of the beam element in global coordinate system are as follows:
Wherein:
5), using the method for solving of Newmark- β step_by_step integration, utilize computer programming, solve above-mentioned steps 3) in pipe
The kinetics equation of column discrete form, and export calculated result.
Newmark- β method assumes first:
In formula, β and γ are the parameters being adjusted by the precision and stability requirement of integral.When β=0.5, γ=0.25
When, it is constant average acceleration method, that is, assumes that the speed of the time Δt from t to t+ is constant, be taken as constantBy
Formula (24) and (25) can obtain:
Consider the oscillatory differential equation of t+ time Δt are as follows:
In formula
Steps are as follows for the calculating of Newmark- β method as a result:
1. initial calculation:
(1) stiffness matrix [K], mass matrix [M] and damping matrix [C] are formed；
(2) initial value { u } is given0,With
(3) integration step Δ t, parameter beta, γ are selected, and calculates integral constant
(4) effective stiffness matrix is formed
2. the calculating pair each time step:
(1) useful load of t+ time Δt is calculated:
(2) displacement of t+ time Δt is solved:
(3) velocity and acceleration of t+ time Δt is calculated:
Newmark- β method is a kind of implicit integration format of unconditional stability, and the size of time step Δ t does not influence to solve
Stability, the selection of Δ t mainly determines that specific calculation flow chart is as shown in Figure 3 according to the precision of solution.
D, it is effectively carried using vertical, horizontal vibration displacement, tubing string axial stress and the tubing string of above-mentioned calculated result analysis tubing string
Lotus.
Embodiment:
By taking the A3 gas well of the Yingge-hai Basin east gas field 13-2 as an example, the well calculating parameter is as shown in table 1:
The 1 east gas field 13-2 A3 gas well calculating parameter of table
| Parameter | Numerical value | Parameter | Numerical value |
| Pipe range (m) | 3900 | Time step (s) | 0.001 |
| Tubing string internal diameter (m) | 0.1003 | Division unit number | 1000 |
| Tubing string outer diameter (m) | 0.1143 | Element length | 3.9 |
| Casing inner diameter (m) | 0.1778 (7 cun of tail pipes) | Coefficient of friction | 0.3 |
| Sleeve outer (m) | 0.1658 | Oil pipe density (kg/m3) | 7850 |
| Fluid velocity (m/s) | 10.0 | Fluid density (kg/m3) | 750 |
| It calculates time (s) | 10 | Hole angle (°) | 43.44 |
| Production packer position (m) | 3588 | Middle packer position (m) | 3900 |
| Tubing material | 15.1ppf13cr-L80 | Tensile strength (MPa) | 665 |
The east gas field 13-2 A3 gas well is directional well, and coordinate is with straight down and horizontally to the right for positive direction, tubing string upper end
For tubing hanger, model is considered as fixing end when calculating, it is at 3588m that production packer, which is located at well depth, and middle packer is located at oil pipe
At 3900m, it is set as fixing end when calculating analysis, tubing string divides 1~1000 node, each node left and right settings bullet from top to bottom
Spring damper, is considered as oil pipe-casing contact-impact boundary condition, and tubing string vibration factor is mainly that fluid flows through bending section generation
Impact force and tubing string itself gravity.It is analyzed by the calculating of model, takes well depth 390m, 1170m, 1950m, 2730m respectively
With the dynamic response (vibration displacement, axial stress and payload) of tubing string at the position 3510m, tubing string vibratory response machine is disclosed
Reason obtains the vibratory response rule of tubing string.
It is illustrated in figure 4 the vibration shape of tubing string different moments transverse direction, tubing string is in the maximum displacement of pit shaft
0.02575m (i.e. left and right maximum displacement in figure).It is found that tubing string is more violent in the vibration of initial stage lower part, touched with casing-contact
It hits more acutely, energy is communicated up from outer sharp power position, and the time is longer, and the vibration shape of entire tubing string is close.
(a)~(e) indicates the transverse vibrational displacement at tubing string different location, due to there is the constraint of casing, tubing string in Fig. 5
Lateral displacement changes between -0.02575m~0.02575m, it is known that, the vibration frequency of the top and bottom of tubing string is higher than tubing string
Medium position, the tubing string when analyzing the fatigue life of tubing string, at selective analysis top and bottom.(f)~(j) is indicated in Fig. 5
Extensional vibration displacement at tubing string different location, since gas well is directional well, inclination angle 43.44oc causes length travel maximum
The medium position of tubing string is appeared in, the extensional vibration frequency of different location is close, close to the longitudinal direction of production packer position tubing string
There is negative value in displacement, illustrates that tubing string is in compressive state, emphasis considers that these positions go out the stability (bending deformation point of tubing string
Analysis).
The tubing string mainly effect by gravity and fluid impingement force, it is larger that the effect of gravity generates tubing string in the axial direction
Stress, while the oscillation crosswise of tubing string also generates axial stress, ultimately forms total axial stress, and the axial direction for obtaining tubing string is answered
Power time-history curves are as shown such as (a)~(e) in Fig. 6.It is found that tubing string is in tensional state in upper end position, stress amplitude reaches
250Mpa, according to the tensile strength of material, tubing string is not destroyed, and therefore, when carrying out tube column strength check, emphasis considers pipe
Whether column upper end position can occur tensile failure；The existing tensile stress of the medium position of tubing string also has a compression, and vibration frequency compared with
Greatly, the fatigue life of this part tubing string of selective analysis；Tubing string is in compressive state in lower end position, and stress is up to
600MPa, emphasis consider whether tubing string can occur bending deformation.
(a)~(e) show the axle power time-history curves of tubing string different location in Fig. 7, it is known that, it is rushed in self gravity and fluid
It hits under the action of power, tubing string top is in tensional state (the axle power direction being subject to is downward), bending deformation is not susceptible to, in well
Tubing string is i.e. by axial tension also by the effect of axial compressive force at the deep position 1950m, in the position well depth 2730m with lower tubular column master
It to be destroyed by the effect of axial compressive force, Yi Fasheng bending deformation.Woods critical load calculation formula is used herein:
Calculating analysis to obtain the Critical Buckling Loads of oblique straight section tubing string according to the parameter in table 1 is 35t, and (e) can in 7
Know, the maximum axle power of tubing string reaches 58t or so, and bending deformation has occurred in tubing string, therefore, should be arranged in the lower position of tubing string
The prevention and control device of bending deformation weakens tubing string and sleeve friction damage and failure.
Fig. 8 shows the moment of flexure time-history curves of different location tubing string, it is known that, the dynamic bending moment amplitude that tubing string goes out in different location
Less, main cause is that casing has effect of contraction to the lateral displacement of tubing string for variation.
High temperature and pressure high gas rate well completion tubular column vibration prediction method provided in this embodiment has the beneficial effect that the present invention
The high temperature and pressure high gas rate well completion tubular column vibration prediction method of offer can by computer programming carry out operation, it is easy to operate,
It calculates quickly, can get the stress condition of any element length tubing string in completion tubular column by this method, through practical proof, the party
Method computational accuracy is also able to satisfy field demand, can be designed high temperature and pressure high-yield well completion tubular column by this method, construction, maintenance
Aspect provides theory support.
The above is not intended to limit the present invention in any form, although the present invention is disclosed with preferred embodiment
As above, however, it is not intended to limit the invention, any person skilled in the art, is not departing from technical solution of the present invention model
In enclosing, when the technology contents using the disclosure above make a little change or are modified to the equivalent embodiment of equivalent variations, in every case
It is the content without departing from technical solution of the present invention, it is to the above embodiments according to the technical essence of the invention any simply to repair
Change, equivalent variations and modification, all of which are still within the scope of the technical scheme of the invention.
Claims (2)
1. a kind of high temperature and pressure high gas rate well completion tubular column vibration prediction method, characterized in that it comprises the following steps:
A, with horizontally to the right for x-axis, well vertical depth direction is y-axis, the longitudinal and lateral coupling kinetic model of tubing string is established, it is total to obtain tubing string
Kinetic energy T, total potential energy U calculating formula difference are as follows:
In formula: L is tubing string length (m)；ρ is tubing string density (kg/m3)；A is tubing string cross-sectional area (m2)；U is tubing string length travel
(m)；W is tubing string lateral displacement (m)；V is tube fluid speed (m/s)；ρoFor fluid density (kg/m in tubing string3)；E is tubing string
Elasticity modulus (MPa)；EI is drilling pipe bending rigidity (Nm2)；T is the time (s)；
B, according to Hamiton's principle, tubing string extensional vibration differential side is derived by the tubing string total kinetic energy T, total potential energy U calculating formula
The calculating formula of journey f (x, t) and tubing string oscillation crosswise differential equation p (x, t) difference are as follows:
C, the longitudinally, laterally oscillatory differential equation of tubing string is solved, and exports calculated result with computer；
D, vertical, horizontal vibration displacement, tubing string axial stress, tubing string payload and the pipe of calculated result analysis tubing string are utilized
Column moment of flexure.
2. high temperature and pressure high gas rate well completion tubular column vibration prediction method according to claim 1, which is characterized in that upper
It states in step C, further comprising the steps of:
1), using linear Lagrangian and hermite function three times, by the length travel u of tubing string and lateral displacement field w
Carry out finite element discretization；
2) the finite element discretization form of the length travel u of tubing string and lateral displacement field w, are substituted into tubing string in the step A always to move
The tubing string total kinetic energy T indicated with displacement of joint vector, the canonical form of total potential energy U, table are obtained in energy T, total potential energy U calculating formula
Distinguish up to formula as follows:
3), the displacement of joint vector form based on the tubing string total kinetic energy T, total potential energy U, further according to variation principle, in conjunction with tubing string
Extensional vibration differential equation f (x, t) and tubing string oscillation crosswise differential equation p (x, t), obtains the kinetics equation of tubing string discrete form
It is as follows:
4), by the coordinate transformation of tubing string in lower curved section to horizontally to the right for x-axis, well vertical depth direction is the whole coordinate in y-axis
In system；
5), using the method for solving of Newmark- β step_by_step integration, using computer programming, solve in the step 3) tubing string from
The kinetics equation for the form of dissipating, and export calculated result.
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| CN113107458A (en) * | 2021-03-15 | 2021-07-13 | 西南石油大学 | High-temperature high-pressure high-yield oil pipe column casing friction wear prediction method |
| CN116776765A (en) * | 2023-05-31 | 2023-09-19 | 西南石油大学 | Method for predicting and preventing failure of dangerous well section of gas-induced vibration tubular column |
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