CN109519166A - Casing strength checking method and device - Google Patents
Casing strength checking method and device Download PDFInfo
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- CN109519166A CN109519166A CN201710833665.4A CN201710833665A CN109519166A CN 109519166 A CN109519166 A CN 109519166A CN 201710833665 A CN201710833665 A CN 201710833665A CN 109519166 A CN109519166 A CN 109519166A
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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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- 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
- E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
Abstract
The present invention provides a kind of casing strength checking method and device.This method includes carrying out the force analysis of the homogeneous state of stress off field to each stress point in combination tube layer, obtains the uniform radial stress and uniform tangential stress of each stress point；The force analysis of deviation stress off field is carried out to each stress point in combination tube layer, obtains the non-homogeneous radial stress, non-homogeneous tangential stress and shear stress of each stress point；According to the uniform radial stress of each stress point, uniform tangential stress, non-homogeneous radial stress, non-homogeneous tangential stress and shear stress, the stress matrix of each stress point in combination jacket layer is obtained；Characteristic value solution is carried out to the stress matrix of each stress point on combination jacket layer middle sleeve, obtains multiple groups characteristic value；According to multiple groups characteristic value, the maximum equivalent of casing is obtained；According to the yield strength of the maximum equivalent of casing and casing, determine whether casing is surrendered.The present invention is able to carry out the accurate verification procedure for carrying out casing strength.
Description
Technical field
The present invention relates to Oil & Gas Drilling Technology field more particularly to a kind of casing strength checking methods and device.
Background technique
Oil/gas well middle sleeve carries the support borehole wall and effect as underground oil and gas transfer passages, to guarantee be drilled well and
Later period oil-gas mining safe and highly efficient operation is most important.In order to guarantee the normal drilling well of oil/gas well and recovery process, need to select peace
Full casing specifications parameter guarantees casing strength.And the selection of casing specifications parameter depends on casing strength checking method, casing
Intensity checking method more meets Geologic Structure Feature and field engineering is practical, and casing specifications parameter more meets Life cycle peace
The requirement of full property.
When calculating the external force that casing is born, traditional sleeve intensity checking method usually assumes that ground of the casing by stratum
Stress is steady state value, and does not take into account that the influence of cement sheath, and therefore, this method necessarily causes to veritify result inaccuracy, so that set
Pipe specifications parameter is unable to satisfy safety requirements.
Summary of the invention
The present invention provides a kind of casing strength checking method and device, to solve traditional sleeve intensity checking method due to not
Consider the influence of cement sheath and set crustal stress suffered by casing to be constant force and lead to not asking for accurate veritification casing strength
Topic.
The present invention provides a kind of casing strength checking method, comprising:
The force analysis of the homogeneous state of stress off field is carried out to each stress point in combination tube layer, obtains the uniform radial direction of each stress point
Stress and uniform tangential stress, wherein the compound tube layer include according to the default arrangement that puts in order at least one casing, with
The identical cement sheath of described sleeve pipe number and stratum, default put in order alternately are arranged for described sleeve pipe and the cement sheath
Column, described sleeve pipe are arranged in innermost layer, and the stratum is arranged in outermost layer；
The force analysis of deviation stress off field is carried out to each stress point in the combination tube layer, obtains the non-equal of each stress point
Even radial stress, non-homogeneous tangential stress and shear stress；
According to the uniform radial stress of each stress point, uniform tangential stress, non-homogeneous radial stress, non-homogeneous tangential stress
And shear stress, obtain the stress matrix of each stress point in the combination jacket layer；
Characteristic value solution is carried out to the stress matrix of each stress point on the combination jacket layer middle sleeve, obtains multiple groups feature
It is worth, includes three principal stresses of described sleeve pipe in every group of characteristic value；
The characteristic value according to multiple groups obtains the maximum equivalent of described sleeve pipe；
According to the yield strength of the maximum equivalent of described sleeve pipe and described sleeve pipe, determine whether described sleeve pipe bends
Clothes.
Optionally, described according to the maximum equivalent of described sleeve pipe and the yield strength of described sleeve pipe, determine the set
Whether pipe is surrendered, comprising:
When described sleeve pipe maximum equivalent be less than described sleeve pipe yield strength, it is determined that described sleeve pipe there is no
Surrender；
When the maximum equivalent of described sleeve pipe is equal to or more than the yield strength of described sleeve pipe, it is determined that described sleeve pipe hair
Raw surrender.
Optionally, the force analysis of the homogeneous state of stress off field is carried out to each stress point in the combination tube layer, comprising:
Connected according to the first radial displacement expression formula, uniform radial stress expression formula, uniform tangential stress expression formula and first
Continuous condition obtains the relational expression of interior contact force and external touch between adjacent contacting layer in the combination tube layer, wherein institute
First condition of continuity is stated to be radial displacement of any stress point on the outer surface of the first contact layer and contact with described first
Radial displacement on the inner surface of the second adjacent contact layer of layer is equal, and first contact layer is to appoint in the assembled casing layer
One contact layer；
It is held according on the outer surface of the interior contact force and the assembled casing born on the inner surface of the assembled casing layer
The external touch received carries out the relational expression of interior contact force and external touch between adjacent contacting layer in the combination tube layer
It solves, obtains in the combination tube layer interior contact force and external touch between adjacent contacting layer；
According to interior contact force and external touch, the uniform radial stress table between adjacent contacting layer in the combination tube layer
Up to formula and the uniform tangential stress expression formula, the uniform radial stress and uniform tangential stress of each stress point are obtained.
Optionally,
The first radial displacement expression formula is obtained by following formula (1) and formula (2):
uri=D εθi/2；Formula (1)；
Wherein, i=1,2 ..., n-1, n are the number of plies of contact layer in the combination jacket layer, and D is that the combination tube layer is taken up an official post
Two times of the distance in the center of circle of plane where one stress point to the stress point, and Di-1≤D≤Di, DiFor the combination tube layer
In two times of the distance in the center of circle of plane where stress point to the stress point on i-th layer of contact layer, Di-1For the combination tube layer
In two times of the distance in the center of circle of plane where stress point to the stress point on (i-1)-th layer of contact layer, uriFor i-th layer of contact layer
Outer surface on stress point the first radial displacement, εθiFor the tangential strain of stress point on i-th layer of contact layer, EiIt is connect for i-th layer
The elasticity modulus of stress point, μ in contact layeriFor the Poisson's ratio of stress point on i-th layer of contact layer, σθiFor stress on i-th layer of contact layer
The uniform tangential stress of point, σriFor the uniform radial stress of stress point on i-th layer of contact layer.
Optionally,
The uniform radial stress expression formula is obtained by following formula (3):
The uniform tangential stress expression formula is obtained by following formula (4):
Wherein, PiStress point is born in the interior contact force born for stress point on i+1 layer contact layer or i-th layer of contact layer
External touch, Pi-1The interior contact force born for stress point on i-th layer of contact layer；
First condition of continuity is obtained by following formula (5):
Wherein, ur(i+1)For the radial displacement of stress point on the inner surface of i+1 layer contact layer；
First condition of continuity is obtained by following formula (6):
AiPi+1-BiPi+CiPi—1=0 formula (6)；
Wherein,
Pi+1For the external touch that stress point on i+1 layer contact layer is born, P0It is drilling fluid in the combination tube layer
The interior contact force that surface generates, Pn=(σH+σh)/2 are the external touch that the outer surface of the combination tube layer is born, σHIt is described
Combine the maximum horizontal principal stress of tube layer, σhFor the minimum horizontal principal stress of the combination tube layer.
It is optionally, described that the force analysis of deviation stress off field is carried out to each stress point in the combination tube layer, comprising:
According to second condition of continuity, First Boundary Condition, second boundary, the second radial displacement expression formula, tangential position
Expression formula, non-homogeneous radial stress expression formula, non-homogeneous tangential stress expression formula and shear stress expression formula are moved, each stress point is obtained
Non-homogeneous radial stress, non-homogeneous tangential stress and shear stress, wherein second condition of continuity is any stress point the
Non-homogeneous radial stress and shear stress on the outer surface of three contact layers connect with the adjacent with the third contact layer the 4th respectively
Non-homogeneous radial stress and shear stress on the inner surface of contact layer is equal, and any stress point is in the appearance of the third contact layer
The radial displacement in face and tangential displacement respectively and with the radial displacement and tangential displacement phase on the inner surface of the 4th contact layer
Deng, the First Boundary Condition be non-homogeneous radial stress of any stress point in the combination jacket layer on most interior contact layer and
Shear stress is zero, and the second boundary is that any stress point is non-homogeneous on outermost contact layer in the combination jacket layer
Radial stress and shear stress are given value, and the third contact layer is any contact layer in the assembled casing layer.
Optionally,
Second condition of continuity is obtained by following formula (7):
Wherein, i=1,2 ..., n-1, n are the number of plies of contact layer in the combination jacket layer, and D is that the combination tube layer is taken up an official post
Two times of the distance in the center of circle of plane where one stress point to the stress point, and Di≤D≤Di+1, DiFor the combination tube layer
In two times of the distance in the center of circle of plane where stress point to the stress point on i-th layer of contact layer, Di+1For the combination tube layer
Two times of the distance in the center of circle of plane where stress point to the stress point, σ ' on middle i+1 layer contact layerriIt is contacted for i-th layer
The non-homogeneous radial stress of stress point, σ ' on layerr(i+1)For the non-homogeneous radial stress of stress point on i+1 layer contact layer, τ 'rθi
For the shear stress of stress point on i-th layer of contact layer, τ 'rθ(i+1)For the shear stress of stress point on i+1 layer contact layer, U 'riFor
Second radial displacement of stress point, U ' on the outer surface of i-th layer of contact layerr(i+1)For stress on the inner surface of i+1 layer contact layer
The radial displacement of point, U 'rθiFor the tangential displacement of stress point on the outer surface of i-th layer of contact layer, U 'rθ(i+1)For the contact of i+1 layer
The tangential displacement of stress point on the inner surface of layer；
The First Boundary Condition is obtained by following formula (8):
Wherein, σ 'r1For the non-homogeneous radial stress of stress point on most interior contact layer in the combination jacket layer, τ 'rθ1It is described
Combine the shear stress of stress point on most interior contact layer in jacket layer, D0For stress point on most interior contact layer in the combination tube layer to institute
Two times of the distance in the center of circle of plane where stating stress point；
The second boundary is obtained by following formula (9):
S=(σH-σh)/2
Wherein, σ 'rnFor the non-homogeneous radial stress of stress point on outermost contact layer in the combination jacket layer, τ 'rθnIt is described
Combine the shear stress of stress point on outermost contact layer in jacket layer, DnFor stress point on outermost contact layer in the combination tube layer to institute
Two times of the distance in the center of circle of plane, σ where stating stress pointHFor the maximum horizontal principal stress of the combination tube layer, σhIt is described group
Close the minimum horizontal principal stress of tube layer；
The second radial displacement expression formula of any stress point on the combination jacket layer is respectively obtained by following formula (10)
With tangential displacement expression formula:
Formula (10)；
Wherein, EiFor the elasticity modulus of stress point on i-th layer of contact layer, μiFor the Poisson of stress point on i-th layer of contact layer
Than, θ for stress point on i-th layer of contact layer and the stress point the center of circle in the plane line and σHBetween angle, Ai′,
Bi′,Ci′,Fi' it is coefficient to be asked, Di-1For where stress point on (i-1)-th layer of contact layer in the combination tube layer to the stress point
Two times of the distance in the center of circle of plane；
The non-homogeneous radial stress expression formula, the non-homogeneous tangential stress table are respectively obtained by following formula (11)
Up to formula and the shear stress expression formula:
σ′ri=-(2Bi′+4Ci′r-2+6Fi′r-4)cos2θ
σ′θi=(12Ai′r2+2Bi′+6Fi′r-4) cos2 θ formula (11).
τ′rθi=(12Ai′r2+2Bi′-2Ci′r-2-6Fi′r-4)cos2θ
Optionally, the stress matrix St of each stress point is indicated by following formula (12) in the combination jacket layer:
Optionally, the maximum equivalent σ of described sleeve pipe is obtained by following formula (13)E:
Wherein, σEFor the maximum equivalent of described sleeve pipe, σ1k,σ2k,σ3kFor three principal stresses of multiple groups of described sleeve pipe, k
For the number of stress point in described sleeve pipe.
The present invention provides also a kind of casing strength and veritifies device, comprising:
Force analysis module is obtained for carrying out the force analysis of the homogeneous state of stress off field to each stress point in combination tube layer
The uniform radial stress and uniform tangential stress of each stress point, wherein the compound tube layer includes according to the default arrangement that puts in order
At least one casing, cement sheath identical with described sleeve pipe number and stratum, it is described it is default put in order as described sleeve pipe and
The cement sheath is alternately arranged, and described sleeve pipe is innermost layer, and the stratum is arranged in outermost layer；
The force analysis module is also used to carry out the stress of deviation stress off field to each stress point in the combination tube layer
Analysis, obtains the non-homogeneous radial stress, non-homogeneous tangential stress and shear stress of each stress point；
Obtain module, for according to the uniform radial stress of each stress point, uniform tangential stress, non-homogeneous radial stress,
Non-homogeneous tangential stress and shear stress obtain the stress matrix of each stress point in the combination jacket layer；
Characteristic value solves module, carries out characteristic value for the stress matrix to each stress point on the combination jacket layer middle sleeve
It solves, obtains multiple groups characteristic value, include three principal stresses of described sleeve pipe in every group of characteristic value；
The acquisition module, is also used to the characteristic value according to multiple groups, obtains the maximum equivalent of described sleeve pipe；
Determining module, described in determining according to the maximum equivalent of described sleeve pipe and the yield strength of described sleeve pipe
Whether casing is surrendered.
Casing strength checking method and device provided by the invention, by will be according to default casing, the cement to put in order
Ring and stratum are regarded as combination jacket layer, can fully consider the characteristic of cement sheath, also more closing to reality drilling condition.Again to group
It closes each stress point in tube layer and carries out the force analysis of uniform stress field and deviation stress off field, obtain the uniform radial direction of each stress point
Stress, uniform tangential stress, non-homogeneous radial stress, non-homogeneous tangential stress and shear stress comprehensively, can be analyzed rapidly
Combine the stress condition of each stress point in jacket layer.Then, according to the uniform radial stress of each stress point, uniform tangential stress, non-
Uniform radial stress, non-homogeneous tangential stress and shear stress, obtain the stress matrix of each stress point.Due to need to only consider on casing
Therefore the stress condition of each stress point only carries out characteristic value solution to the stress matrix of stress point each on casing, can obtain more
Group characteristic value, wherein multiple groups characteristic value is able to reflect total distribution of force of each stress point on casing.Then, by multiple groups feature
Value solves the equivalent stress of casing, chooses maximum equivalent and is compared with casing strength, can determine whether casing occurs
Surrender.Casing, cement sheath and stratum are regarded as combination jacket layer by the present invention, no matter not only fully consider the number of plies of practical casing
It is that single layer casing or multilayer sleeve can fully consider cement sheath feature, additionally it is possible to which analysis obtains total stress point of casing
Cloth also solves the problem of existing method can not accurately veritify casing strength, realizes the accurate casing specification ginseng for determining and choosing
Whether number can satisfy the safety requirements design of Life cycle.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of assembly jacket layer in casing strength checking method provided by the invention；
Fig. 2 is the flow diagram one of casing strength checking method provided by the invention；
Fig. 3 is the flow diagram two of casing strength checking method provided by the invention；
Fig. 4 is the effect diagram one of casing strength checking method provided by the invention；
Fig. 5 a is the effect diagram two of casing strength checking method provided by the invention；
Fig. 5 b is the effect diagram three of casing strength checking method provided by the invention；
Fig. 5 c is the effect diagram four of casing strength checking method provided by the invention；
Fig. 6 a is the effect diagram five of casing strength checking method provided by the invention；
Fig. 6 b is the effect diagram six of casing strength checking method provided by the invention；
Fig. 6 c is the effect diagram seven of casing strength checking method provided by the invention；
Fig. 7 is the structural schematic diagram that casing strength provided by the invention veritifies device.
Specific embodiment
Fig. 1 is the structural schematic diagram of assembly jacket layer in casing strength checking method provided by the invention, and Fig. 2 is this hair
The flow diagram one of the casing strength checking method of bright offer, Fig. 3 are the stream of casing strength checking method provided by the invention
Journey schematic diagram two.During actual well drilled operation or production operation, the crustal stress that stratum generates can be transferred to set by cement sheath
Pipe, therefore, the characteristic of cement sheath can have an impact casing strength.In order to comprehensive and accurately veritify casing strength, this implementation
Example can will regard one as according at least one casing, cement sheath identical with casing number and the stratum of the default arrangement that puts in order
Cyclic annular cylinder, i.e. combination tube layer, and casing, cement sheath and stratum need to meet to preset and put in order, wherein default put in order
It is alternately arranged for casing and cement sheath, sleeve arrangement is arranged in outermost layer on innermost layer, stratum.The present embodiment middle sleeve can be single
Layer can also be multilayer, and the present embodiment does not limit this, and need to only meet casing and put in order according to default.Such as Fig. 1 institute
Show, for ease of description, three layers of casing, three layers of cement sheath and stratum may be selected in the combination jacket layer of the present embodiment.Its middle sleeve,
The geometric dimension on cement sheath and stratum and intensive parameter are shown in Table 1.Under normal conditions, the diameter on stratum is about the interior of innermost layer casing
10 times of diameter.
The geometric dimension and intensive parameter of 1 casing of table, cement sheath and stratum
| Outer diameter (mm) | Elasticity modulus (G Pa) | Poisson's ratio | |
| Internal diameter | 152.5 | ||
| Casing 1 | 177.8 | 210 | 0.3 |
| Cement sheath 1 | 220.72 | 10 | 0.23 |
| Casing 2 | 244.7 | 210 | 0.3 |
| Cement sheath 2 | 315.34 | 10 | 0.23 |
| Casing 3 | 365.12 | 210 | 0.3 |
| Cement sheath 3 | 444.5 | 10 | 0.23 |
| Stratum | 3000 | 8 | 0.28 |
Further, the strata condition in assembly jacket layer is complicated and changeable, and therefore, the crustal stress that stratum generates can also occur
Variation.For time saving and quickly veritify casing strength, the danger that the present embodiment can select casing that may surrender according to strata condition
Dangerous well section is veritified.Skilled person will appreciate that when stratum it is more liquid when, stratum generate crustal stress be easy to make
Casing surrender is obtained, such as stratum is saline bed, rock stratum etc..When there is tomography in stratum, the crustal stress that stratum generates is larger, also holds
It is easier that casing is surrendered.Therefore, the strong corresponding dangerous well section of formation mobility can be only selected in the present embodiment, it can also only selectively
The high dangerous well section of layer ground stress anomally, also can formation mobility is strong and ground stress anomally is high dangerous well section.The present embodiment pair
This is without limitation.
For example, the present embodiment can specifically select dangerous well according to the seismic data on stratum locating for well and strata division situation
Section, as shown in table 2.The well will meet Kumugeliemu group saline bed in 2550-6450 meters of brills, and this well section makes since creep acts on
It obtains casing and bears biggish crustal stress, therefore, the dangerous well section for surrendering this well section as potential casing in the present embodiment.
2 strata division table of table
Further, since default put in order simulates actual casing programme and actual well drilled operating condition, this reality
Apply combined in example tube layer can more closing to reality situation, can not only be influenced in view of cement sheath bring, so that casing strength
It is more accurate to veritify result, additionally it is possible to veritify to multilayer sleeve intensity.Meanwhile the present embodiment can also be in conjunction with earthquake and survey
Well data obtain the higher region crustal stress of precision and rock mechanics parameters, can be veritified in the dangerous well section that casing is surrendered,
It can save and calculate the time, and improve and calculate accuracy.
Specifically, it is in the casing of certain depth in the earth formation, linear deformation can be very small, and the present embodiment can not consider
The variation of crustal stress along longitudinal direction can be asked plane strain is converted into the strain problems occurred on each stress point in combination tube layer
Topic, as shown in Figure 1.Assume that casing, cement sheath and stratum are circular ideal in the present embodiment, and thickness is uniform.
Further, in this embodiment each stress point can be subject to according to the stress of each stress point in combination tube layer
All stress are divided into two parts: uniform parts and non-uniform part.Specifically can by solving uniform parts and non-uniform part, then
According to principle of stacking, to uniform parts and it is non-be superimposed with part disengaging after obtain the total stress distribution of each stress point.Such as Fig. 2 institute
Show, the method for the present embodiment may include:
S101, the force analysis of the homogeneous state of stress off field is carried out to each stress point in combination tube layer, obtains the equal of each stress point
Even radial stress and uniform tangential stress.
Further, in this embodiment different modes can be used, pass through off field pair in the homogeneous state of stress that uniform parts generate
The force analysis of each stress point obtains the uniform radial stress and uniform tangential stress of each stress point.In order to obtain each stress point
Uniform radial stress and uniform tangential stress, the present embodiment carries out the specific implementation process of the force analysis of each stress point detailed
It describes in detail bright.As shown in figure 3, this method further include:
S1011, by the first radial displacement expression formula, uniform radial stress expression formula, uniform tangential stress expression formula and
One condition of continuity obtains the relational expression of interior contact force and external touch between adjacent contacting layer in combination tube layer, wherein the
One condition of continuity is radial displacement of any stress point on the outer surface of the first contact layer and adjacent with the first contact layer
Radial displacement on the inner surface of second contact layer is equal, and the first contact layer is any contact layer in assembled casing layer.
It is born on the outer surface of the interior contact force and assembled casing born on S1012, the inner surface according to assembled casing layer
External touch, to the relational expression of interior contact force and external touch solves between adjacent contacting layer in combination tube layer,
Obtain in combination tube layer interior contact force and external touch between adjacent contacting layer.
S1013, according to combining in tube layer, interior contact force and external touch, uniform radial stress are expressed between adjacent contacting layer
In formula and uniform tangential stress expression formula, the uniform radial stress and uniform tangential stress of each stress point are obtained.
Specifically, the first radial displacement expression formula can be obtained by following formula (1) and formula (2) in the present embodiment:
uri=D εθi/2；Formula (1)；
Wherein, i=1,2 ..., n-1, n are the number of plies for combining contact layer in jacket layer, and D is that combination tube layer is taken up an official post a stress point
Two times of the distance in the center of circle of plane where to the stress point, and Di-1≤D≤Di, DiFor on i-th layer of contact layer in combination tube layer
Two times of distance to the center of circle of plane where the stress point of stress point, Di-1For in combination tube layer on (i-1)-th layer of contact layer by
Two times of distance to the center of circle of plane where the stress point of force, uriFor the diameter of stress point on the outer surface of i-th layer of contact layer
To displacement, εθiFor the tangential strain of stress point on i-th layer of contact layer, EiFor the elasticity modulus of stress point on i-th layer of contact layer, μi
For the Poisson's ratio of stress point on i-th layer of contact layer, σθiFor the uniform tangential stress of stress point on i-th layer of contact layer, σriIt is i-th
The uniform radial stress of stress point on layer contact layer.
Uniform radial stress expression formula is obtained by following formula (3):
Uniform tangential stress expression formula is obtained by following formula (4):
Wherein, PiStress point is born in the interior contact force born for stress point on i+1 layer contact layer or i-th layer of contact layer
External touch, Pi-1The interior contact force born for stress point on i-th layer of contact layer.
First condition of continuity is obtained by following formula (5):
Wherein, ur(i+1)For the radial displacement of stress point on the inner surface of i+1 layer contact layer；
First condition of continuity is obtained by following formula (6):
AiPi+1-BiPi+CiPi—1=0 formula (6)；
Wherein,
Pi+1For the external touch that stress point on i+1 layer contact layer is born, P0It is drilling fluid to the inner surface of combination tube layer
The interior contact force generated, Pn=(σH+σh)/2 are the external touch for combining the outer surface of tube layer and bearing, σHMost for combination tube layer
Big horizontal principal stress, σhFor the minimum horizontal principal stress for combining tube layer.
Further, due in adjacent contacting layer, position of any stress point on the wherein inner surface of a contact layer
Setting the position on the outer surface with another contact layer is the same position, therefore, diameter of the stress point on adjacent contacting layer
It is equal to being displaced, and be subject on the interior contact force that is subject on a wherein contact layer of the stress point and another contact layer outer
Contact force is equal.Based on the above process, the present embodiment can first be substituted into formula (1), formula (2), formula (3) and formula (4)
In formula (5), formula (6) are obtained, wherein formula (6) is about PiN-1 member system of linear equations.Then, due to assembled casing
The interior contact force born on the inner surface of layer is exactly the interior contact force P that drilling fluid generates the inner surface of combination tube layer0It can pass through
The prior art measures, and the external touch born on the outer surface of assembled casing be exactly combine tube layer outer surface bear it is external
Touch Pn=(σH+σh)/2, wherein the maximum horizontal principal stress σ of combination tube layerHWith the minimum horizontal principal stress σ of combination tube layerh?
It can be measured by the prior art, therefore, the outer surface of the interior contact force and assembled casing born on the inner surface of assembled casing layer
The external touch of upper receiving is given value, and the present embodiment can connect by the way that solve the n-1 of n-layer contact layer in formula (6) unknown
Touch Pi, then by PiIt is updated in formula (3) and formula (4), just can obtain combining each stress in tube layer under uniform stress field
The stress distribution of point, that is, be calculated the uniform radial stress and uniform tangential stress of each stress point.
S102, the force analysis of deviation stress off field is carried out to each stress point in combination tube layer, obtains the non-of each stress point
Uniform radial stress, non-homogeneous tangential stress and shear stress.
Specifically, different modes can be used in the present embodiment, passes through off field in the unequal stress that non-uniform part generates
To the force analysis of each stress point, non-homogeneous radial stress, non-homogeneous tangential stress and shear stress are obtained.In order to obtain each stress
Non-homogeneous radial stress, non-homogeneous tangential stress and the shear stress of point, the present embodiment are specific to the force analysis of each stress point
Realization process is described in detail.
Optionally, according to second condition of continuity, First Boundary Condition, second boundary, the second radial displacement expression formula
With tangential displacement expression formula, the non-homogeneous radial stress, non-homogeneous tangential stress expression formula and shear stress table of each stress point are obtained
Up to formula, wherein second condition of continuity is that non-homogeneous radial stress of any stress point on the outer surface of third contact layer and cutting is answered
Power respectively and on the inner surface of the 4th adjacent contact layer of third contact layer non-homogeneous radial stress and shear stress it is equal, and
Inner surface of any stress point in the radial displacement of the outer surface of third contact layer and tangential displacement respectively and with the 4th contact layer
On radial displacement and tangential displacement it is equal, First Boundary Condition is any stress point in combination jacket layer on most interior contact layer
Non-homogeneous radial stress and shear stress are zero, and second boundary is any stress point in combination jacket layer on outermost contact layer
Non-homogeneous radial stress and shear stress be given value, third contact layer is any contact layer in assembled casing layer.
Specifically, the present embodiment can obtain second condition of continuity by following formula (7):
Wherein, i=1,2 ..., n-1, n are the number of plies for combining contact layer in jacket layer, and D is that combination tube layer is taken up an official post a stress point
Two times of the distance in the center of circle of plane where to the stress point, and Di≤D≤Di+1, DiFor on i-th layer of contact layer in combination tube layer
Two times of distance to the center of circle of plane where the stress point of stress point, Di+1For stress on i+1 layer contact layer in combination tube layer
Two times of the distance in the center of circle of plane, σ ' where point arrives the stress pointriNon-homogeneous radial direction for stress point on i-th layer of contact layer is answered
Power, σ 'r(i+1)For the non-homogeneous radial stress of stress point on i+1 layer contact layer, τ 'rθiFor stress point on i-th layer of contact layer
Shear stress, τ 'rθ(i+1)For the shear stress of stress point on i+1 layer contact layer, U 'riFor stress on the outer surface of i-th layer of contact layer
Second radial displacement of point, U 'r(i+1)For the radial displacement of stress point on the inner surface of i+1 layer contact layer, U 'rθiIt is i-th layer
The tangential displacement of stress point, U ' on the outer surface of contact layerrθ(i+1)For on the inner surface of i+1 layer contact layer stress point it is tangential
Displacement.
First Boundary Condition is obtained by following formula (8):
Wherein, σ 'r1For the non-homogeneous radial stress of stress point on most interior contact layer in combination jacket layer, τ 'rθ1To combine jacket layer
In on most interior contact layer stress point shear stress, D0It is flat where stress point to the stress point on most interior contact layer in combination tube layer
Two times of the distance in the center of circle in face.
Second boundary is obtained by following formula (9):
S=(σH-σh)/2
Wherein, σ 'rnFor the non-homogeneous radial stress of stress point on outermost contact layer in combination jacket layer, τ 'rθnTo combine jacket layer
In on outermost contact layer stress point shear stress, DnIt is flat where stress point to the stress point on outermost contact layer in combination tube layer
Two times of the distance in the center of circle in face, σHFor the maximum horizontal principal stress for combining tube layer, σhIt is answered to combine the minimum level master of tube layer
Power.
The second radial displacement expression formula of any stress point on combination jacket layer is respectively obtained by following formula (10) and is cut
To displacement expression formula:
Formula (10)；
Wherein, EiFor the elasticity modulus of stress point on i-th layer of contact layer, μiFor the Poisson of stress point on i-th layer of contact layer
Than, θ for stress point on i-th layer of contact layer and the stress point the center of circle in the plane line and σHBetween angle, A 'i,Bi′,
Ci′,Fi' it is coefficient to be asked, Di-1For stress point on (i-1)-th layer of contact layer in combination tube layer to the center of circle of plane where the stress point
Two times of distance.
Non-homogeneous radial stress expression formula, non-homogeneous tangential stress expression formula are respectively obtained by following formula (11) and are cut
Stress expression formula:
σ′ri=-(2Bi′+4Ci′r-2+6Fi′r-4)cos2θ
σ′θi=(12Ai′r2+2Bi′+6Fi′r-4) cos2 θ formula (11).
τ′rθi=(12Ai′r2+2Bi′-2Ci′r-2-6Fi′r-4)cos2θ
Further, due in adjacent contacting layer, position of any stress point on the wherein inner surface of a contact layer
Setting the position on the outer surface with another contact layer is the same position, and assumes that casing, cement sheath and stratum completely attach to,
Therefore, radial displacement and tangential displacement of the stress point on the surfaces externally and internally of adjacent contacting layer is equal, and the stress point exists
The non-homogeneous radial stress being subject on the outer surface of one of contact layer and it is subject on the inner surface of another contact layer non-
Uniform radial stress is equal, the shear stress and another contact layer which is subject on the wherein outer surface of a contact layer
Inner surface on the shear stress that is subject to it is also equal.Moreover, because the outermost layer of assembled casing is stratum, therefore the present embodiment can benefit
The maximum horizontal principal stress σ born stratum outer surface is measured with the prior artHWith minimum horizontal principal stress σh, then pass through public affairs
Formula (9) can obtain the non-homogeneous radial stress σ ' of stress point on outermost contact layer in combination jacket layerrnWith shear stress τ 'rθn, because
This, non-homogeneous radial stress and shear stress of any stress point in combination jacket layer on outermost contact layer are given value.
Further, since second condition of continuity, First Boundary Condition, second boundary can determine undetermined coefficient
Ai′,Bi′,Ci′,Fi', therefore, the present embodiment can simultaneous formula (7), formula (8), formula (9), formula (10) and formula (11)
Obtain coefficient A to be askedi′,Bi′,Ci′,Fi′.It then, will coefficient A be askedi′,Bi′,Ci′,Fi' be updated in formula (11),
It obtains combining the stress distribution of each stress point in tube layer off field in deviation, that is, the non-homogeneous radial direction that each stress point is calculated is answered
Power, non-homogeneous tangential stress and shear stress.
Herein it should be noted that S101 can be executed prior to S102, S102 can also be executed prior to S101, S101 and S102
Also can be performed simultaneously, the present embodiment to the execution of S101 and S102 sequence without limitation.
S103, according to the uniform radial stress of each stress point, uniform tangential stress, non-homogeneous radial stress, non-homogeneous cut
To stress and shear stress, the stress matrix of each stress point in combination jacket layer is obtained.
Specifically, each stress on combination jacket layer in the uniform parts of each stress point has been obtained by S101, passed through
S102 has also obtained each stress on combination jacket layer in the non-uniform part of each stress point.The present embodiment can by uniform parts and
Stress in non-uniform part radially is overlapped, and by uniform parts and non-uniform part it is tangential on stress fold
Be subject to and uniform parts and non-uniform part in shear stress be overlapped principle, using matrix obtain combination jacket layer in each stress
The stress matrix of point, stress matrix are used to indicate the total stress distribution of each stress point.
Optionally, the stress matrix St for combining each stress point in jacket layer is indicated by following formula (12):
S104, characteristic value solution is carried out to the stress matrix of each stress point on combination jacket layer middle sleeve, obtains multiple groups feature
It is worth, includes three principal stresses of casing in every group of characteristic value.
S105, according to multiple groups characteristic value, obtain the maximum equivalent of casing.
Specifically, in order to veritify casing strength, the present embodiment only needs to know the stress condition of each stress point on casing, energy
Enough save the time.Due to casing combination jacket layer in position be it is known, using Matrix Solving characteristic value in the present embodiment
Method, especially by stress point each on casing stress matrix solve characteristic value, obtain the multiple groups characteristic value of casing, wherein
Include three principal stresses of casing in every group of characteristic value, and three principal stresses be able to reflect on current state setting of casing some by
The stress condition in force.In this way, multiple groups characteristic value is able to reflect total distribution of force of each stress point on casing.
Further, in this embodiment can substitute into multiple groups characteristic value in formula (13), the multiple groups for calculating casing are equivalent
Stress.It is strong due to during actually veritifying casing strength, need to only veritify maximum equivalent stress and casing surrender on casing
Therefore, in the present embodiment the size of degree can choose maximum value as maximum equivalent in all equivalent stress.Optionally,
The maximum equivalent σ of casing is obtained by following formula (13)E:
Wherein, σEFor the maximum equivalent of casing, σ1k,σ2k,σ3kFor three principal stresses of multiple groups of casing, k is casing
The number of upper stress point.
S106, according to the maximum equivalent of casing and the yield strength of casing, determine whether casing is surrendered.
It specifically, can be true by the comparison of the maximum equivalent of casing and the yield strength of casing in the present embodiment
Whether the casing specifications parameter chosen surely meets safety requirements.Optionally, when the maximum equivalent of casing is less than bending for casing
Take intensity, it is determined that there is no surrender, the casing specifications parameters of selection to meet safety requirements for casing；When the maximum equivalent of casing
Stress is equal to or more than the yield strength of casing, it is determined that casing is surrendered, and the casing specifications parameter of selection is unsatisfactory for safety
It is required that.
Casing strength checking method provided in this embodiment, by by according to the default casing to put in order, cement sheath and
Stratum is regarded as combination jacket layer, can fully consider the characteristic of cement sheath, also more closing to reality drilling condition.Again to compound tube
Each stress point carries out the force analysis of uniform stress field and deviation stress off field on layer, and the uniform radial direction for obtaining each stress point is answered
Power, uniform tangential stress, non-homogeneous radial stress, non-homogeneous tangential stress and shear stress, can comprehensively, rapidly analyze group
The stress condition of each stress point in trap layer.Then, according to the uniform radial stress of each stress point, uniform tangential stress, it is non-
Even radial stress, non-homogeneous tangential stress and shear stress, obtain the stress matrix of each stress point.It is each on casing due to need to only consider
Therefore the stress condition of stress point only carries out characteristic value solution to the stress matrix of stress point each on casing, can obtain multiple groups
Characteristic value, wherein multiple groups characteristic value is able to reflect total distribution of force of each stress point on casing.Then, by multiple groups characteristic value
The equivalent stress of casing is solved, maximum equivalent is chosen and is compared with casing strength, can determine whether casing bends
Clothes.Casing, cement sheath and stratum are regarded as combination jacket layer by the present embodiment, no matter not only fully consider the number of plies of practical casing
It is that single layer casing or multilayer sleeve can fully consider cement sheath feature, additionally it is possible to which analysis obtains total stress point of casing
Cloth also solves the problem of existing method can not accurately veritify casing strength, realizes the accurate casing specification ginseng for determining and choosing
Whether number can satisfy the safety requirements design of Life cycle.
Fig. 4 is the effect diagram one of casing strength checking method provided by the invention, and Fig. 5 a is set provided by the invention
The effect diagram two of pipe intensity checking method, Fig. 5 b are the effect diagram of casing strength checking method provided by the invention
Three, Fig. 5 c are the effect diagram four of casing strength checking method provided by the invention, and Fig. 6 a is that casing provided by the invention is strong
The effect diagram five of checking method is spent, Fig. 6 b is the effect diagram six of casing strength checking method provided by the invention, figure
6c is the effect diagram seven of casing strength checking method provided by the invention.On the basis of the above embodiments, the present embodiment
The verification procedure under various drilling conditions to casing strength can be met.For example, being unloaded in creep, cementing quality reduction and wellbore pressure
In the case of carrying three kinds, all achievable veritification to casing strength of the present embodiment.As Figure 4-Figure 6, to three layers of set as shown in Figure 2
The specific implementation process that pipe intensity is veritified is described in detail.
Firstly, three layers of casing have been calculated in the present embodiment before and after bearing creep effect, the casing of different depth well section
The situation of change of maximum equivalent.As shown in figure 4, the maximum equivalent of casing increases with the increase of well section depth,
And after considering creep effect, maximum equivalent increases more obvious.For three layers of casing, outer layer sleeve
(365.12mm casing) bears always maximum equivalent stress, is also most likely to occur surrender.In a practical situation, outer layer sleeve
Using TP140 grade of steel, yield strength 956.265MPa.The outermost layer set being calculated using the method for the present embodiment
Maximum equivalent is 484.8MPa after the creep that pipe is born, be much smaller than its yield strength, it is contemplated that after creep effect,
Each layer casing is able to maintain safety, and sleeve design parameter also meets safety requirements.
Secondly, well cementation can be simulated by the reduction of cement sheath elasticity modulus in the present embodiment such as Fig. 5 a, Fig. 5 b and Fig. 5 c
The situation that quality reduces calculates the variation feelings of the casing maximum equivalent of different depth well section using the method for the present embodiment
Condition.
If Fig. 5 a is shown, the maximum equivalent of outer layer sleeve (365.12mm casing) can be with cement sheath elastic model
First increases and then decreases is reduced, and reaches maximum when cement sheath elasticity modulus reduces by 80%, and its value is 649MPa.
As shown in Figure 5 b, intermediate casing (244.7mm casing) layer by layer is born with the reduction of cement sheath elasticity modulus
Maximum equivalent is gradually reduced, and has maximum equivalent to reach maximum at ideal cementing quality, value 304.9MPa.
As shown in Figure 5 c, inner layer sleeve (177.8mm casing) is with the reduction of cement sheath elasticity modulus, the maximum born
Equivalent stress first reduces and increases afterwards, be maximum equivalent is minimum value when cementing quality reduces by 40% or so, and it is maximum
Equivalent stress is much smaller than casing yield strength.
Further, when cementing quality declines, three layers of casing can be calculated using the method for the present embodiment and born most
Big equivalent stress completes the process that casing strength is veritified.
Finally, such as Fig. 6 a, Fig. 6 b and Fig. 6 c, it can be by drilling fluid density in reduction well come simulation wellbore hole pressure in the present embodiment
The situation of power unloading can be specifically 1.85g/cm in the drilling fluid density upper limit3, drilling fluid density lower limit be 1.75g/cm3, pit shaft
Empty (0g/cm entirely3) and pit shaft empty 70% (0.55g/cm3) in the case of these four, calculated not using the method for the present embodiment
With the situation of change of the casing equivalent stress of depth well section.In wellbore pressure unloading, calculated using the method for the present embodiment
To the maximum equivalent born of three layers of casing be less than the yield strength of casing, meet casing safety requirement.
Further, by creep effect, the specific verification process that cementing quality reduces and wellbore pressure unloads, show this
Embodiment can realize the checking procedure under different complex working conditions to casing strength, and the method for the present embodiment is more in line with live work
Cheng Shiji, and it is able to carry out the casing specification parameter designing for meeting safety requirements.
Fig. 7 is the structural schematic diagram that casing strength provided by the invention veritifies device.As shown in fig. 7, the dress of the present embodiment
It sets and may include:
Force analysis module 10 is obtained for carrying out the force analysis of the homogeneous state of stress off field to each stress point in combination tube layer
To the uniform radial stress and uniform tangential stress of each stress point, wherein the compound tube layer includes putting in order according to default
At least one casing, cement sheath identical with described sleeve pipe number and the stratum of column, described preset put in order as described sleeve pipe
It is alternately arranged with the cement sheath, described sleeve pipe is innermost layer, and the stratum is arranged in outermost layer；
The force analysis module 10, be also used to carry out each stress point in the combination tube layer deviation stress off field by
Power analysis, obtains the non-homogeneous radial stress, non-homogeneous tangential stress and shear stress of each stress point；
Module 20 is obtained, for answering according to the uniform radial stress, uniform tangential stress, non-homogeneous radial direction of each stress point
Power, non-homogeneous tangential stress and shear stress obtain the stress matrix of each stress point in the combination jacket layer；
Characteristic value solves module 30, carries out feature for the stress matrix to each stress point on the combination jacket layer middle sleeve
Value solves, and obtains multiple groups characteristic value, includes three principal stresses of described sleeve pipe in every group of characteristic value；
The acquisition module 20, is also used to the characteristic value according to multiple groups, obtains the maximum equivalent of described sleeve pipe；
Determining module 40, for determining institute according to the maximum equivalent of described sleeve pipe and the yield strength of described sleeve pipe
State whether casing is surrendered.
Optionally, the determining module 40 is less than described sleeve pipe specifically for the maximum equivalent when described sleeve pipe
Yield strength, it is determined that there is no surrenders for described sleeve pipe；
When the maximum equivalent of described sleeve pipe is equal to or more than the yield strength of described sleeve pipe, it is determined that described sleeve pipe hair
Raw surrender.
Optionally, the force analysis module 10 is specifically used for according to the first radial displacement expression formula, uniform radial stress
Expression formula, uniform tangential stress expression formula and first condition of continuity are obtained in the combination tube layer and are inscribed between adjacent contacting layer
The relational expression of touch and external touch, wherein first condition of continuity is appearance of any stress point in the first contact layer
Radial displacement on face and in, institute equal with the radial displacement on the inner surface of the second adjacent contact layer of first contact layer
Stating the first contact layer is any contact layer in the assembled casing layer；
It is held according on the outer surface of the interior contact force and the assembled casing born on the inner surface of the assembled casing layer
The external touch received carries out the relational expression of interior contact force and external touch between adjacent contacting layer in the combination tube layer
It solves, obtains in the combination tube layer interior contact force and external touch between adjacent contacting layer；
According to interior contact force and external touch, the uniform radial stress table between adjacent contacting layer in the combination tube layer
Up to formula and the uniform tangential stress expression formula, the uniform radial stress and uniform tangential stress of each stress point are obtained.
Optionally,
The first radial displacement expression formula is obtained by following formula (1) and formula (2):
uri=D εθi/2；Formula (1)；
Wherein, i=1,2 ..., n-1, n are the number of plies of contact layer in the combination jacket layer, and D is that the combination tube layer is taken up an official post
Two times of the distance in the center of circle of plane where one stress point to the stress point, and Di-1≤D≤Di, DiFor the combination tube layer
In two times of the distance in the center of circle of plane where stress point to the stress point on i-th layer of contact layer, Di-1For the combination tube layer
In two times of the distance in the center of circle of plane where stress point to the stress point on (i-1)-th layer of contact layer, uriFor i-th layer of contact layer
Outer surface on stress point the first radial displacement, εθiFor the tangential strain of stress point on i-th layer of contact layer, EiIt is connect for i-th layer
The elasticity modulus of stress point, μ in contact layeriFor the Poisson's ratio of stress point on i-th layer of contact layer, σθiFor stress on i-th layer of contact layer
The uniform tangential stress of point, σriFor the uniform radial stress of stress point on i-th layer of contact layer.
Optionally,
The uniform radial stress expression formula is obtained by following formula (3):
The uniform tangential stress expression formula is obtained by following formula (4):
Wherein, PiStress point is born in the interior contact force born for stress point on i+1 layer contact layer or i-th layer of contact layer
External touch, Pi-1The interior contact force born for stress point on i-th layer of contact layer；
First condition of continuity is obtained by following formula (5):
Wherein, ur(i+1)For the radial displacement of stress point on the inner surface of i+1 layer contact layer；
First condition of continuity is obtained by following formula (6):
AiPi+1-BiPi+CiPi—1=0 formula (6)；
Wherein,
Pi+1For the external touch that stress point on i+1 layer contact layer is born, P0It is drilling fluid in the combination tube layer
The interior contact force that surface generates, Pn=(σH+σh)/2 are the external touch that the outer surface of the combination tube layer is born, σHIt is described
Combine the maximum horizontal principal stress of tube layer, σhFor the minimum horizontal principal stress of the combination tube layer.
Optionally, the force analysis module 10 is specifically also used to according to second condition of continuity, First Boundary Condition,
It is two boundary conditions, the second radial displacement expression formula, tangential displacement expression formula, non-homogeneous radial stress expression formula, non-homogeneous tangential
Stress expression formula and shear stress expression formula obtain the non-homogeneous radial stress, non-homogeneous tangential stress and shear stress of each stress point,
Wherein second condition of continuity is that non-homogeneous radial stress of any stress point on the outer surface of third contact layer and cutting is answered
Power is respectively and non-homogeneous radial stress and shear stress phase on the inner surface of the 4th contact layer adjacent with the third contact layer
Deng, and any stress point connects in the radial displacement of the outer surface of the third contact layer and tangential displacement respectively and with the described 4th
Radial displacement and tangential displacement on the inner surface of contact layer is equal, and the First Boundary Condition is any stress point in the combination
Non-homogeneous radial stress and shear stress in jacket layer on most interior contact layer are zero, and the second boundary is any stress point
Non-homogeneous radial stress and shear stress in the combination jacket layer on outermost contact layer are given value, the third contact layer
For any contact layer in the assembled casing layer.
Optionally,
Second condition of continuity is obtained by following formula (7):
Wherein, i=1,2 ..., n-1, n are the number of plies of contact layer in the combination jacket layer, and D is that the combination tube layer is taken up an official post
Two times of the distance in the center of circle of plane where one stress point to the stress point, and Di≤D≤Di+1, DiFor the combination tube layer
In two times of the distance in the center of circle of plane where stress point to the stress point on i-th layer of contact layer, Di+1For the combination tube layer
Two times of the distance in the center of circle of plane where stress point to the stress point, σ ' on middle i+1 layer contact layerriIt is contacted for i-th layer
The non-homogeneous radial stress of stress point, σ ' on layerr(i+1)For the non-homogeneous radial stress of stress point on i+1 layer contact layer, τ 'rθi
For the shear stress of stress point on i-th layer of contact layer, τ 'rθ(i+1)For the shear stress of stress point on i+1 layer contact layer, U 'riFor
Second radial displacement of stress point, U ' on the outer surface of i-th layer of contact layerr(i+1)For stress on the inner surface of i+1 layer contact layer
The radial displacement of point, U 'rθiFor the tangential displacement of stress point on the outer surface of i-th layer of contact layer, U 'rθ(i+1)For the contact of i+1 layer
The tangential displacement of stress point on the inner surface of layer；
The First Boundary Condition is obtained by following formula (8):
Wherein, σ 'r1For the non-homogeneous radial stress of stress point on most interior contact layer in the combination jacket layer, τ 'rθ1It is described
Combine the shear stress of stress point on most interior contact layer in jacket layer, D0For stress point on most interior contact layer in the combination tube layer to institute
Two times of the distance in the center of circle of plane where stating stress point；
The second boundary is obtained by following formula (9):
S=(σH-σh)/2
Wherein, σ 'rnFor the non-homogeneous radial stress of stress point on outermost contact layer in the combination jacket layer, τ 'rθnIt is described
Combine the shear stress of stress point on outermost contact layer in jacket layer, DnFor stress point on outermost contact layer in the combination tube layer to institute
Two times of the distance in the center of circle of plane, σ where stating stress pointHFor the maximum horizontal principal stress of the combination tube layer, σhIt is described group
Close the minimum horizontal principal stress of tube layer；
The second radial displacement expression formula of any stress point on the combination jacket layer is respectively obtained by following formula (10)
With tangential displacement expression formula:
Formula (10)；
Wherein, EiFor the elasticity modulus of stress point on i-th layer of contact layer, μiFor the Poisson of stress point on i-th layer of contact layer
Than, θ for stress point on i-th layer of contact layer and the stress point the center of circle in the plane line and σHBetween angle, Ai′,
Bi′,Ci′,Fi' it is coefficient to be asked, Di-1For where stress point on (i-1)-th layer of contact layer in the combination tube layer to the stress point
Two times of the distance in the center of circle of plane；
The non-homogeneous radial stress expression formula, the non-homogeneous tangential stress table are respectively obtained by following formula (11)
Up to formula and the shear stress expression formula:
σ′ri=-(2Bi′+4Ci′r-2+6Fi′r-4)cos2θ
σ′θi=(12Ai′r2+2Bi′+6Fi′r-4) cos2 θ formula (11).
τ′rθi=(12Ai′r2+2Bi′-2Ci′r-2-6Fi′r-4)cos2θ
Optionally, the stress matrix St of each stress point is indicated by following formula (12) in the combination jacket layer:
Optionally, the maximum equivalent σ of described sleeve pipe is obtained by following formula (13)E:
Wherein, σEFor the maximum equivalent of described sleeve pipe, σ1k,σ2k,σ3kFor three principal stresses of multiple groups of described sleeve pipe, k
For the number of stress point in described sleeve pipe.
Casing strength provided in an embodiment of the present invention veritifies device, and above method embodiment can be performed, and specific implementation is former
Reason and technical effect, reference can be made to above method embodiment, details are not described herein again for the present embodiment.
Those of ordinary skill in the art will appreciate that: realize that all or part of the steps of above-mentioned each method embodiment can lead to
The relevant hardware of program instruction is crossed to complete.Program above-mentioned can be stored in a computer readable storage medium.The journey
When being executed, execution includes the steps that above-mentioned each method embodiment to sequence；And storage medium above-mentioned include: ROM, RAM, magnetic disk or
The various media that can store program code such as person's CD.
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (10)
1. a kind of casing strength checking method characterized by comprising
The force analysis of the homogeneous state of stress off field is carried out to each stress point in combination tube layer, obtains the uniform radial stress of each stress point
With uniform tangential stress, wherein the compound tube layer include according to the default arrangement that puts in order at least one casing, with it is described
The identical cement sheath of casing number and stratum, default put in order are alternately arranged for described sleeve pipe and the cement sheath, institute
Sleeve arrangement is stated in innermost layer, the stratum is arranged in outermost layer；
The force analysis of deviation stress off field is carried out to each stress point in the combination tube layer, obtains the non-homogeneous diameter of each stress point
To stress, non-homogeneous tangential stress and shear stress；
According to the uniform radial stress of each stress point, uniform tangential stress, non-homogeneous radial stress, non-homogeneous tangential stress and cut
Stress obtains the stress matrix of each stress point in the combination jacket layer；
Characteristic value solution is carried out to the stress matrix of each stress point on the combination jacket layer middle sleeve, obtains multiple groups characteristic value, often
It include three principal stresses of described sleeve pipe in group characteristic value；
The characteristic value according to multiple groups obtains the maximum equivalent of described sleeve pipe；
According to the yield strength of the maximum equivalent of described sleeve pipe and described sleeve pipe, determine whether described sleeve pipe surrenders.
2. the method according to claim 1, wherein the maximum equivalent according to described sleeve pipe and described
The yield strength of casing, determines whether described sleeve pipe surrenders, comprising:
When the maximum equivalent of described sleeve pipe is less than the yield strength of described sleeve pipe, it is determined that there is no bending for described sleeve pipe
Clothes；
When the maximum equivalent of described sleeve pipe is equal to or more than the yield strength of described sleeve pipe, it is determined that described sleeve pipe occurs to bend
Clothes.
3. the method according to claim 1, wherein carrying out the homogeneous state of stress to stress point each in the combination tube layer
Force analysis off field, comprising:
According to the first radial displacement expression formula, uniform radial stress expression formula, uniform tangential stress expression formula and the first continuous strip
Part obtains the relational expression of interior contact force and external touch between adjacent contacting layer in the combination tube layer, wherein described the
One condition of continuity be radial displacement of any stress point on the outer surface of the first contact layer and with the first contact layer phase
Radial displacement on the inner surface of the second adjacent contact layer is equal, and first contact layer is any in the assembled casing layer connects
Contact layer；
According to what is born on the outer surface of the interior contact force and the assembled casing born on the inner surface of the assembled casing layer
External touch seeks the relational expression of interior contact force and external touch between adjacent contacting layer in the combination tube layer
Solution obtains in the combination tube layer interior contact force and external touch between adjacent contacting layer；
According to interior contact force and external touch, the uniform radial stress expression formula between adjacent contacting layer in the combination tube layer
With the uniform tangential stress expression formula, the uniform radial stress and uniform tangential stress of each stress point are obtained.
4. according to the method described in claim 3, it is characterized in that,
The first radial displacement expression formula is obtained by following formula (1) and formula (2):
uri=D εθi/2；Formula (1)；
Wherein, i=1,2 ..., n-1, n be it is described combination jacket layer in contact layer the number of plies, D be the combination tube layer take up an official post one by
Two times of the distance in the center of circle of plane where force to the stress point, and Di-1≤D≤Di, DiIt is in the combination tube layer i-th
Two times of the distance in the center of circle of plane where stress point to the stress point, D on layer contact layeri-1It is in the combination tube layer
Two times of the distance in the center of circle of plane where stress point to the stress point, u on i-1 layers of contact layerriFor the outer of i-th layer of contact layer
First radial displacement of stress point, ε on surfaceθiFor the tangential strain of stress point on i-th layer of contact layer, EiFor i-th layer of contact layer
The elasticity modulus of upper stress point, μiFor the Poisson's ratio of stress point on i-th layer of contact layer, σθiFor stress point on i-th layer of contact layer
Uniform tangential stress, σriFor the uniform radial stress of stress point on i-th layer of contact layer.
5. according to the method described in claim 4, it is characterized in that,
The uniform radial stress expression formula is obtained by following formula (3):
The uniform tangential stress expression formula is obtained by following formula (4):
Wherein, PiWhat stress point was born in the interior contact force born for stress point on i+1 layer contact layer or i-th layer of contact layer is outer
Contact force, Pi-1The interior contact force born for stress point on i-th layer of contact layer；
First condition of continuity is obtained by following formula (5):
Wherein, ur(i+1)For the radial displacement of stress point on the inner surface of i+1 layer contact layer；
First condition of continuity is obtained by following formula (6):
AiPi+1-BiPi+CiPi—1=0 formula (6)；
Wherein,
Pi+1For the external touch that stress point on i+1 layer contact layer is born, P0It is drilling fluid to the inner surface of the combination tube layer
The interior contact force generated, Pn=(σH+σh)/2 are the external touch that the outer surface of the combination tube layer is born, σHFor the combination
The maximum horizontal principal stress of tube layer, σhFor the minimum horizontal principal stress of the combination tube layer.
6. the method according to claim 1, wherein described carry out deviation to stress point each in the combination tube layer
Force analysis under stress field, comprising:
According to second condition of continuity, First Boundary Condition, second boundary, the second radial displacement expression formula, tangential displacement table
Up to formula, non-homogeneous radial stress expression formula, non-homogeneous tangential stress expression formula and shear stress expression formula, the non-of each stress point is obtained
Uniform radial stress, non-homogeneous tangential stress and shear stress, wherein second condition of continuity is that any stress point connects in third
Non-homogeneous radial stress and shear stress on the outer surface of contact layer are respectively and fourth contact layer adjacent with the third contact layer
Inner surface on non-homogeneous radial stress and shear stress it is equal, and any stress point is in the outer surface of the third contact layer
Radial displacement and tangential displacement respectively and on the inner surface of the 4th contact layer radial displacement and tangential displacement it is equal, institute
Stating First Boundary Condition is that non-homogeneous radial stress of any stress point in the combination jacket layer on most interior contact layer and cutting is answered
Power is zero, and the second boundary is non-homogeneous radial direction of any stress point in the combination jacket layer on outermost contact layer
Stress and shear stress are given value, and the third contact layer is any contact layer in the assembled casing layer.
7. according to the method described in claim 6, it is characterized in that,
Second condition of continuity is obtained by following formula (7):
Wherein, i=1,2 ..., n-1, n be it is described combination jacket layer in contact layer the number of plies, D be the combination tube layer take up an official post one by
Two times of the distance in the center of circle of plane where force to the stress point, and Di≤D≤Di+1, DiIt is in the combination tube layer i-th
Two times of the distance in the center of circle of plane where stress point to the stress point, D on layer contact layeri+1It is in the combination tube layer i-th
Two times of the distance in the center of circle of plane where stress point to the stress point, σ on+1 layer of contact layerr′iFor on i-th layer of contact layer by
The non-homogeneous radial stress in force, σr′(i+1)For the non-homogeneous radial stress of stress point on i+1 layer contact layer, τr′θiIt is i-th
The shear stress of stress point, τ on layer contact layerr′θ(i+1)For the shear stress of stress point on i+1 layer contact layer, Ur′iIt is connect for i-th layer
Second radial displacement of stress point, U on the outer surface of contact layerr′(i+1)For the diameter of stress point on the inner surface of i+1 layer contact layer
To displacement, Ur′θiFor the tangential displacement of stress point on the outer surface of i-th layer of contact layer, Ur′θ(i+1)For in i+1 layer contact layer
The tangential displacement of stress point on surface；
The First Boundary Condition is obtained by following formula (8):
Wherein, σr′1For the non-homogeneous radial stress of stress point on most interior contact layer in the combination jacket layer, τr′θ1For the combination
In jacket layer on most interior contact layer stress point shear stress, D0For stress point on most interior contact layer in the combination tube layer to it is described by
Two times of the distance in the center of circle of plane where force；
The second boundary is obtained by following formula (9):
Wherein, σr′nFor the non-homogeneous radial stress of stress point on outermost contact layer in the combination jacket layer, τr′θnFor the combination
In jacket layer on outermost contact layer stress point shear stress, DnFor stress point on outermost contact layer in the combination tube layer to it is described by
Two times of the distance in the center of circle of plane, σ where forceHFor the maximum horizontal principal stress of the combination tube layer, σhFor the compound tube
The minimum horizontal principal stress of layer；
The second radial displacement expression formula of any stress point on the combination jacket layer is respectively obtained by following formula (10) and is cut
To displacement expression formula:
Wherein, EiFor the elasticity modulus of stress point on i-th layer of contact layer, μiFor the Poisson's ratio of stress point on i-th layer of contact layer, θ is
On i-th layer of contact layer stress point and the stress point the center of circle in the plane line and σHBetween angle, Ai′,Bi′,Ci′,
Fi' it is coefficient to be asked, Di-1For plane where stress point to the stress point on (i-1)-th layer of contact layer in the combination tube layer
Two times of the distance in the center of circle；
The non-homogeneous radial stress expression formula, the non-homogeneous tangential stress expression formula are respectively obtained by following formula (11)
With the shear stress expression formula:
8. the method according to claim 1, wherein the stress matrix St of each stress point is logical in the combination jacket layer
Cross following formula (12) expression:
9. the method according to claim 1, wherein obtaining the maximum etc. of described sleeve pipe by following formula (13)
Efficacy σE:
Wherein, σEFor the maximum equivalent of described sleeve pipe, σ1k,σ2k,σ3kFor three principal stresses of multiple groups of described sleeve pipe, k is institute
State the number of stress point on casing.
10. a kind of casing strength veritifies device characterized by comprising
Force analysis module, for carrying out the force analysis of the homogeneous state of stress off field to each stress point in combination tube layer, obtain respectively by
The uniform radial stress and uniform tangential stress in force, wherein the compound tube layer includes putting in order arrangement extremely according to default
A few casing, cement sheath identical with described sleeve pipe number and stratum, described preset put in order as described sleeve pipe and described
Cement sheath is alternately arranged, and described sleeve pipe is innermost layer, and the stratum is arranged in outermost layer；
The force analysis module is also used to carry out deviation stress stress off field point to each stress point in the combination tube layer
Analysis, obtains the non-homogeneous radial stress, non-homogeneous tangential stress and shear stress of each stress point；
Obtain module, for according to the uniform radial stress of each stress point, uniform tangential stress, non-homogeneous radial stress, it is non-
Even tangential stress and shear stress obtain the stress matrix of each stress point in the combination jacket layer；
Characteristic value solves module, carries out characteristic value for the stress matrix to each stress point on the combination jacket layer middle sleeve and asks
Solution, obtains multiple groups characteristic value, includes three principal stresses of described sleeve pipe in every group of characteristic value；
The acquisition module, is also used to the characteristic value according to multiple groups, obtains the maximum equivalent of described sleeve pipe；
Determining module, for determining described sleeve pipe according to the maximum equivalent of described sleeve pipe and the yield strength of described sleeve pipe
Whether surrender.
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| CN201710833665.4A CN109519166A (en) | 2017-09-15 | 2017-09-15 | Casing strength checking method and device |
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| CN105765164A (en) * | 2013-11-27 | 2016-07-13 | 兰德马克绘图国际公司 | Determining stresses in a pipe under non-uniform exterior loads |
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| US20110308788A1 (en) * | 2010-06-16 | 2011-12-22 | Halliburton Energy Services, Inc. | Controlling well operations based on monitored parameters of cement health |
| CN105765164A (en) * | 2013-11-27 | 2016-07-13 | 兰德马克绘图国际公司 | Determining stresses in a pipe under non-uniform exterior loads |
| CN105760564A (en) * | 2014-12-19 | 2016-07-13 | 中国石油天然气股份有限公司 | Method and device for analyzing oil-string casing failure |
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