CN107194098B - Oil-gas pipeline pipe stress-strain curve equation fitting method based on probability distribution - Google Patents

Oil-gas pipeline pipe stress-strain curve equation fitting method based on probability distribution Download PDF

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CN107194098B
CN107194098B CN201710397860.7A CN201710397860A CN107194098B CN 107194098 B CN107194098 B CN 107194098B CN 201710397860 A CN201710397860 A CN 201710397860A CN 107194098 B CN107194098 B CN 107194098B
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stress
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oil
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CN107194098A (en
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刘玉卿
张振永
余志峰
佟雷
李朝
赵子峰
刘绍兴
张智禹
武玉梁
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China National Petroleum Corp
China Petroleum Pipeline Engineering Corp
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Abstract

The invention relates to a method for fitting an oil and gas pipeline pipe stress-strain curve equation based on probability distribution, which comprises the steps of respectively determining a probability density function and a distribution function of yield strength and tensile strength of an oil and gas pipeline pipe, calculating the yield strength and the tensile strength of the pipe, calculating the yield ratio lambda, the stress hardening index n and the yield offset α of the pipe, and fitting the stress-strain curve Ramberg-Osgood equation of the pipe.

Description

Oil-gas pipeline pipe stress-strain curve equation fitting method based on probability distribution
Technical Field
The invention relates to a method for fitting a stress-strain curve equation of an oil and gas pipeline pipe based on probability distribution, in particular to a method for fitting a Ramberg-Osgood equation of a stress-strain curve of an oil and gas pipeline pipe based on probability distribution, and belongs to the field of material performance, structural design and strength evaluation of oil and gas pipelines.
Background
In the transportation, construction, operation and maintenance processes of the oil and gas pipeline, the external conditions are complex and changeable, and the deformation or damage of the pipe body such as bending, deformation, cracking and the like is inevitable. For example, a pipe passing through a section where surface displacement may occur, such as an active fault, a slope, a goaf, and soft soil, may be bent and deformed in response to the surface displacement. After the pipeline is deformed or damaged, a certain safety margin is always provided, and the pipeline can be continuously used after the residual strength evaluation. In order to determine the safety margin after deformation and damage of the pipeline, the pipeline is generally required to be evaluated, and the stress-strain curve of the pipe is the most commonly used basic performance parameter in the evaluation of the pipeline.
Generally, it is recommended in the specifications to determine the stress-strain curve of a pipe experimentally. This method is less operable: firstly, in order to maintain the integrity of a calculation pipe section, a sample cannot be cut on the calculation pipe section to measure and calculate the stress-strain curve of the pipe section; secondly, even if a sample can be cut for measurement, the stress-strain curve of the local pipe cannot represent the stress-strain curve of the whole pipeline due to the nonuniformity of the performance of the pipe; and thirdly, a simple and easy-to-use mathematical expression is difficult to obtain according to the actually measured stress-strain curve. The performance error of the pipe causes the evaluation result of the residual strength of the pipeline to generate a large difference with the actual situation, and the evaluation result with consistent reliability is difficult to obtain; the mathematical expression is difficult to fit, and great inconvenience is brought to engineering application.
How to obtain the stress-strain curve equation which is consistent in reliability, simple and easy to use, and further evaluate the pipeline is a technical problem to be solved urgently in the field of evaluation of material performance, structural design and strength of oil and gas pipelines.
Disclosure of Invention
In order to solve the problem of tubing performance value in the fields of oil and gas pipeline tubing performance, structural design and strength evaluation, the invention aims to provide a probability distribution-based tubing stress-strain curve equation fitting method for an oil and gas pipeline, which comprises a tubing yield strength and tensile strength value-taking method based on probability distribution and a stress-strain curve Ramberg-Osgood equation fitting method.
The invention is realized by the following technical scheme:
a method for fitting an oil and gas pipeline pipe stress-strain curve equation based on probability distribution comprises the following steps:
step 1, calculating the distribution type of the yield strength of pipe sections in the same batch or same steel grade according to an oil-gas pipeline, and determining the probability density function f of the yield strength of the pipe1(t) and distribution function F1(σy)；
Determining an expected yield θ of pipe yield strength1And calculating the expected yield theta according to the following formula1Lower corresponding pipe yield strength sigmay：
Figure BDA0001308951200000021
Step 2, calculating the distribution type of the tensile strength of the same batch or same steel grade pipe of the pipe section according to the oil-gas pipeline, and determining the probability density function f of the tensile strength of the pipe2(t) and distribution function F2(σu)；
Determining the expected yield theta of tensile strength of a pipe2And calculating the expected yield theta according to the following formula2Lower corresponding tensile strength sigma of pipeu：
Figure BDA0001308951200000022
Step 3, according to the yield strength sigma of the pipeyAnd tensile strength sigma of pipeuCalculating the yield ratio lambda of the pipe:
Figure BDA0001308951200000023
step 4, calculating the stress hardening index n of the pipe according to the yield ratio lambda of the pipe:
Figure BDA0001308951200000024
step 5, calculating the yield offset α of the pipe according to the following formula:
Figure BDA0001308951200000025
in the formula: e is the elastic modulus of the pipe;
and 6, fitting a pipe stress-strain curve Ramberg-Osgood equation as follows:
Figure BDA0001308951200000031
in the formula: ε is the strain of the pipe and σ is the stress of the pipe.
The invention has the beneficial effects that:
the method for fitting the stress-strain curve equation of the oil and gas pipeline pipe based on probability distribution enables pipeline designers to calculate the yield strength and the tensile strength of the pipe which meet the expected qualification rate requirement and have consistent reliability by adopting the probability distribution method, and fits the stress-strain curve Ramberg-Osgood equation of the pipe. The method is simple to implement, can obtain the Ramberg-Osgood equation of the stress-strain curve of the pipe meeting the expected qualification rate requirement and having consistent reliability, has simple and easy-to-use equation expression, is easy to master by extensive pipeline operation managers and designers, and can be widely applied to the field of evaluation of the performance, structural design and strength of the oil and gas pipeline pipe.
Drawings
FIG. 1 is a longitudinal stress-strain curve of X80 steel-grade natural gas long-distance pipeline pipes and a Ramberg-Osgood equation thereof obtained in the example of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the invention is illustrated by taking the longitudinal stress-strain curve of the X80 steel-grade natural gas long-distance pipeline and the Ramberg-Osgood equation thereof as an example.
(1) Pipe parameters, as shown in table 1:
TABLE 1X 80 longitudinal performance of steel grade natural gas long-distance pipeline
Figure BDA0001308951200000032
(2) The distribution type of the longitudinal yield strength of the pipe is normal distribution as follows:
1) probability density function f of normal distribution1(t) is:
Figure BDA0001308951200000041
in the formula: μ is the mathematical expectation of yield strength, μ ═ 615.1 MPa; σ is the standard deviation of yield strength, and σ is 51.5 MPa.
2) Distribution function F of normal distribution1(σy) Comprises the following steps:
Figure BDA0001308951200000042
3) assuming that 95% of yield strength values meeting the X80 steel grade pipeline longitudinal yield strength standards are obtained, namely the expected qualification rate theta of the yield strength1＝95％。
4) Solving for σ according toyCan obtain σy＝530MPa。
Figure BDA0001308951200000043
(3) The distribution type of the tensile strength of the pipe is lognormal distribution, and the distribution type is as follows:
1) probability density function f of lognormal distribution2(t) is:
Figure BDA0001308951200000044
in the formula: μ is the mathematical expectation of tensile strength, μ ═ 700.5 MPa; σ is the standard deviation of tensile strength, and σ is 45.5 MPa.
2) Distribution function F of lognormal distribution2(σu) Comprises the following steps:
Figure BDA0001308951200000045
3) assuming that 95% of X80 steel grade pipeline pipes are required to obtain tensile strength values meeting the standards in longitudinal tensile strength, namely the expected qualification rate theta of the tensile strength2＝95％。
4) Solving for σ according touCan obtain σu＝628MPa。
Figure BDA0001308951200000046
(4) The yield ratio λ of the pipe was calculated as follows:
Figure BDA0001308951200000047
(5) the stress hardening index n of the pipe is calculated as follows:
Figure BDA0001308951200000048
(6) the yield offset α of the pipe is calculated as follows:
Figure BDA0001308951200000051
(7) fitting a stress-strain curve Ramberg-Osgood equation, namely a sigma-epsilon equation, as follows:
Figure BDA0001308951200000052
wherein epsilon is the strain of the pipe; sigma is the stress of the pipe, MPa.
(8) According to the stress-strain curve Ramberg-Osgood equation, a longitudinal stress-strain curve of the X80 steel-grade natural gas long-distance pipeline is drawn and is shown in figure 1.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A method for fitting an oil and gas pipeline pipe stress-strain curve equation based on probability distribution is characterized by comprising the following steps:
step 1, calculating the distribution type of the yield strength of pipe sections in the same batch or same steel grade according to an oil-gas pipeline, and determining the probability density function f of the yield strength of the pipe1(t) and distribution function F1(σy)；
Determining an expected yield θ of pipe yield strength1And calculating the expected yield theta according to the following formula1Lower corresponding pipe yield strength sigmay：
Figure FDA0002419909740000011
Step 2, calculating the distribution type of the tensile strength of the same batch or same steel grade pipe of the pipe section according to the oil-gas pipeline, and determining the probability density function f of the tensile strength of the pipe2(t) and distribution function F2(σu)；
Determining the expected yield theta of tensile strength of a pipe2And calculating the expected yield theta according to the following formula2Lower corresponding tensile strength sigma of pipeu：
Figure FDA0002419909740000012
Step 3, according to the yield strength sigma of the pipeyAnd tensile strength σuCalculating the yield ratio lambda of the pipe:
Figure FDA0002419909740000013
step 4, calculating the stress hardening index n of the pipe according to the yield ratio lambda of the pipe:
Figure FDA0002419909740000014
step 5, calculating the yield offset α of the pipe according to the following formula:
Figure FDA0002419909740000015
in the formula: e is the Young modulus of the pipe;
and 6, fitting a pipe stress-strain curve Ramberg-Osgood equation as follows:
Figure FDA0002419909740000016
in the formula: ε is the strain of the pipe and σ is the stress of the pipe.
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CN109752240A (en) * 2019-02-28 2019-05-14 郑州建斌电子科技有限公司 A kind of automatic testing method of diamond fretsaw yield stress
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CN113705030B (en) * 2020-05-20 2024-03-26 中国石油天然气集团有限公司 Method, device, equipment and storage medium for determining lifting amount of oil and gas pipeline
CN112304740A (en) * 2020-09-27 2021-02-02 中国石油天然气集团有限公司 Strength detection and calculation method of three-way pipe fitting
CN116227282B (en) * 2023-02-01 2023-12-08 中国石油大学(北京) Method and equipment for determining stress-strain relation parameters of girth weld zone material

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