CN108830491A - A kind of drilling failure relative risk appraisal procedure - Google Patents

A kind of drilling failure relative risk appraisal procedure Download PDF

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CN108830491A
CN108830491A CN201810647835.4A CN201810647835A CN108830491A CN 108830491 A CN108830491 A CN 108830491A CN 201810647835 A CN201810647835 A CN 201810647835A CN 108830491 A CN108830491 A CN 108830491A
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function
density
node
value
appraisal procedure
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沈建文
王旭东
李林
黄胜强
睢圣
黄屋宇
杨峰
康力
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Sinopec Oilfield Service Corp
Drilling Engineering Research Institute of Sinopec Southwest Petroleum Engineering Co Ltd
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Sinopec Oilfield Service Corp
Drilling Engineering Research Institute of Sinopec Southwest Petroleum Engineering Co Ltd
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Abstract

The invention discloses a kind of drilling failure relative risk appraisal procedure, the appraisal procedure includes the following steps：Step 1. density points multiple in situ of drilling well random acquisition；Density points collected are smoothed by step 2. using spline function, obtain smooth density function curve, this density function curve has secondary lead can micro- characteristic；Step 3. is programmed processing by the obtained density function curve of step 2, in the method for finite integral, obtains the integrated value of density function curve；Step 4. assesses underground risk probability using the integrated value of step 3 density function curve obtained.The present invention can obtain the drilling failure relative risk of higher reliability and confidence level.

Description

A kind of drilling failure relative risk appraisal procedure
Technical field
The present invention relates to the appraisal procedures of the drilling failure relative risk in oil-gas exploration and development.
Background technique
In oil-gas exploration and development, particularly in the drilling process of ultradeep well, easily there is card drain spray and the drilling failures such as collapses, This, which just needs to draft early period in wellbore construction, designs corresponding drilling plan, so as in subsequent specific wellbore construction process In, it can be by the drilling failure of generation reliable reply, control without any confusion, for example, when brill meets easy loss horizon, high pressure is easily gushed When layer position or easy slough formation position, it on the one hand can use the effective sealing complex accident layer position of casing, on the other hand can pass through It controls drilling fluid density and efficiently controls formation fluid and flow to pit shaft etc..
The design of drilling plan needs to be likely encountered the size of accident risk rate in clear drilling process, by drilling well Accident risk rate defines, and can just design reliable, complete drilling plan, that is to say, that the assessment of drilling failure relative risk Whether reliable, the reliability and integrality of drilling plan design directly decide, be that the design of drilling plan has greatly It helps, directive significance.
Currently, the appraisal procedure of drilling failure relative risk mainly has angular distribution probability density method and normal distribution probability method Two kinds.Wherein, the characteristics of angular distribution probability density method is three characteristic values for needing to find drilling fluid density, respectively minimum Value, most probable value and maximum value, the Density Distribution of the stochastic variable can be evaluated with this, three numerical value may make up a triangle Distribution, carrying out integral to angular distribution can be obtained risk probability.Normal distribution probability method is to carry out sample using multiple samples Statistics calculates density sample variance, determines drilling risk probability using normal distribution table.These appraisal procedures need to rely on It is expected in specific density points, density, the factor of density variance equivalence, be to have points probabilistic based on selection data, Therefore, be using the density function that aforementioned special value is established it is uncertain, this will lead to assess drilling well thing obtained Therefore the reliability of risk probability and confidence level are lower, are unsuitable for the drilling failure risk probability of various Complex Blocks, different intervals Assessment.
Summary of the invention
Technical purpose of the invention is：In view of the above shortcomings of the prior art, it provides a kind of without dependent on specific close Point, density expectation, density variance equivalence factor are spent, commenting for the drilling failure relative risk of higher reliability and confidence level can be obtained Estimate method.
The present invention realizes its technical purpose the technical scheme adopted is that a kind of drilling failure relative risk appraisal procedure, It is characterized in that, the appraisal procedure includes the following steps：
Step 1. density points multiple in situ of drilling well random acquisition；
Density points collected are smoothed by step 2. using spline function, and it is bent to obtain smooth density function Line, this density function curve have secondary lead can micro- characteristic；
Step 3. is programmed processing by the obtained density function curve of step 2, in the method for finite integral, obtains close Spend the integrated value of function curve；
Step 4. assesses underground risk probability using the integrated value of step 3 density function curve obtained.
The density points acquired in step 1 are >=3.
The specific acquisition process of density function curve in above-mentioned steps 2 is：
If it is known that function y=f (x) is in node a=x0<x1<…<xn=b, yi=f (xi), i=0,1,2 ..., at n Functional value and derivative value are yi=f (xi), i=0,1,2 ..., n；
If S (x) meets condition, S (x) is the cubic polynomial and s of a segmentationi(x)=yi, S (x) has at [a, b] Second Order Continuous derivative, then claiming S (x) is spline interpolation function, and the concrete form of S (x) is：
Wherein, Si(x) in [xn-1,xn] on be cubic polynomial Si(x)=aix3+bix2+cix+di；
By interpolation condition S (xi)=yi, i=0,1,2 ..., n obtain n+1 condition；
Boundary condition one is S ' (x0)=y0′,S′(xn)=yn′；
Boundary condition two is S " (x0)=y0″,S″(xn)=yn″；
Boundary condition three is that assumed function y=f (x) is periodic function using b-a as the period, it is desirable that S (x) is also period letter Number, i.e.,：
In each subinterval [xn-1,xn], because it is an order polynomial that S (x), which is cubic polynomial, S " (x), it is assumed that Node xiLocate S " (xi)=Mi, i=0,1,2 ..., n, then in [xn-1,xn] on：
Twice to above formula integral：
Wherein, CiAnd DiValue be respectively arbitrary constant, acquired by endpoint value, MiUsing spline function in node xiPlace's single order is led Number continuously determines.
The specific acquisition process of the integrated value of density function curve in above-mentioned steps 3 is：
Design integrating range [a, b] is divided into n equal portions, step-lengthChoose Equidistant Nodes xkWhat=a+kh was constructed inserts Value type quadrature formula is：
In formula,For cotes coefficients, x=a+th is enabled, is had：
As n=2, had by above formula：
It is by upper formula complexification：
It is rewritten as：
The method have the benefit that：The above method is the density points that arrive situ of drilling well random acquisition by batten Interpolating function is smoothed, to obtain the density function curve not constrained by density points, then to not in a manner of finite integral It is programmed processing by the density function curve that density points constrain, the integrated value for obtaining density function curve carries out down-hole accident wind The assessment of dangerous probability, need not dependent on specific density point, density expectation, density variance equivalence factor, can obtain it is higher can By the drilling failure relative risk of property and confidence level, have the characteristics that it is simple and easy, easy for construction, low in cost, have a wide range of application.
Specific embodiment
The present invention relates to the appraisal procedures of the drilling failure relative risk in oil-gas exploration and development, below to technology of the invention Content is clearly and detailedly illustrated.
The present invention includes the following steps：
Step 1. is preferably >=3 in the multiple density points of situ of drilling well random acquisition, the quantity of acquired density points；
Density points collected are smoothed by step 2. using spline function, and it is bent to obtain smooth density function Line, this density function curve have it is secondary lead can micro- characteristic, detailed process is：
If it is known that function y=f (x) is in node a=x0<x1<…<xn=b, yi=f (xi), i=0,1,2 ..., at n Functional value and derivative value are yi=f (xi), i=0,1,2 ..., n；In preceding formula：Y is functional value；F (x) is mapping rule；A is The upper limit；xoFor variable at node 0；x1For variable at node 1；xnFor variable at node n；B is lower limit；yiFor function at node i Value；f(xi) it is functional value in variable at node i；
If S (x) meets condition, S (x) is the cubic polynomial and s of a segmentationi(x)=yi, S (x) has at [a, b] Second Order Continuous derivative, then claiming S (x) is spline interpolation function, and the concrete form of S (x) is：
Wherein, Si(x) in [xn-1,xn] on be cubic polynomial Si(x)=aix3+bix2+cix+di；
By interpolation condition S (xi)=yi, i=0,1,2 ..., n obtain n+1 condition；
Boundary condition one is S ' (x0)=y0′,S′(xn)=yn′；
Boundary condition two is S " (x0)=y0″,S″(xn)=yn″；
Boundary condition three is that assumed function y=f (x) is periodic function using b-a as the period, it is desirable that S (x) is also period letter Number, i.e.,：
In above formula：S (x) is smooth function；SiIt (x) is the smooth function at node i；yiFor in variable at i node Functional value；A is the upper limit；B is lower limit；S1It (x) is the smooth function at node 1；X is variable；xoFor variable at node 0；x1 For variable at node 1；S2It (x) is the smooth function at node 2；SnIt (x) is the smooth function at node n；xn-1For node Variable at n-1；xnFor variable at node n；aiFor the upper limit at node i；biFor lower limit at node i；ciFor quadratic power system at node i Number；diFor constant at node i；S ' (x0) it is smooth function first order derivative at node 0；Y '0It is once led for smooth function at node 0 Numerical value；S ' (xn) it is smooth function first order derivative at node n；yn' is smooth function first order derivative value at node n；S ＂ (x0) it is knot Smooth function second derivative at point 0；Y ＂0For smooth function second derivative value at node 0；S ＂ (xn) it is smooth function two at node n Subderivative；yn＂ is smooth function first order derivative value at node n；Y is smooth function；F (x) is smooth function correspondence rule；
In each subinterval [xn-1,xn], because it is an order polynomial that S (x), which is cubic polynomial, S " (x), it is assumed that Node xiLocate S " (xi)=Mi, i=0,1,2 ..., n, then in [xn-1,xn] on：
Twice to above formula integral：
Wherein, MiUsing spline function in node xiPlace's first derivative continuously determines；
In above formula：S ＂ (xi) it is smooth function second derivative at node i；MiFor smooth function second derivative at node i Value；Smooth function second derivative when being x that S ＂ (x) is variable；X is variable；xiFor variate-value at node i；hiFor step-length at node i； S1(x) be variable x when smooth function；CiAnd DiValue be respectively arbitrary constant, acquired by endpoint value；
Step 3. is programmed processing by the obtained density function curve of step 2, in the method for finite integral, obtains close The integrated value of function curve is spent, detailed process is：
Design integrating range [a, b] is divided into n equal portions, step-lengthChoose Equidistant Nodes xkWhat=a+kh was constructed inserts Value type quadrature formula is：
In formula,For cotes coefficients, x=a+th is enabled, is had：
As n=2, had by above formula：
In above formula：A is the upper limit；B is lower limit；N is node；xkFor x value at node k；K is node variable；H is step It is long；I is equivalent variations value；f(xk) it is functional value at node k；X is variable；T is integration variable；J is node；D is differential；c0 (2) For the c0 value at node 2；c1 (2)For the c1 value at node 2；c2 (2)For the c2 value at node 2；
It is by upper formula complexification：
It is rewritten as：
Step 4. assesses underground risk probability using the integrated value of step 3 density function curve obtained.
The above various embodiments is only to illustrate the present invention, rather than its limitations；Although referring to the various embodiments described above to this hair It is bright to be described in detail, those skilled in the art should understand that：The present invention still can be to the various embodiments described above In specific technical solution modify perhaps equivalent replacement of some of the technical features and these modifications or replace It changes, the spirit and scope of the present invention that it does not separate the essence of the corresponding technical solution.

Claims (4)

1. a kind of drilling failure relative risk appraisal procedure, which is characterized in that the appraisal procedure includes the following steps：
Step 1. is in the multiple density points of situ of drilling well random acquisition；
Density points collected are smoothed by step 2. using spline function, obtain smooth density function curve, this Density function curve has secondary lead can micro- characteristic；
Step 3. is programmed processing by the obtained density function curve of step 2, in the method for finite integral, obtains density letter The integrated value of number curve；
Step 4. assesses underground risk probability using the integrated value of step 3 density function curve obtained.
2. drilling failure relative risk appraisal procedure according to claim 1, which is characterized in that the density points acquired in step 1 It is >=3.
3. drilling failure relative risk appraisal procedure according to claim 1, which is characterized in that the density function in step 2 is bent The specific acquisition process of line is：
If it is known that function y=f (x) is in node a=x0<x1<…<xn=b, yi=f (xi), i=0,1,2 ..., the function at n Value and derivative value are yi=f (xi), i=0,1,2 ..., n；
If S (x) meets condition, S (x) is the cubic polynomial and s of a segmentationi(x)=yi, S (x) [a, b] have second order Continuous derivative, then claiming S (x) is spline interpolation function, and the concrete form of S (x) is：
Wherein, Si(x) in [xn-1,xn] on be cubic polynomial Si(x)=aix3+bix2+cix+di；
By interpolation condition S (xi)=yi, i=0,1,2 ..., n obtain n+1 condition；
Boundary condition one is S ' (x0)=y0′,S′(xn)=yn′；
Boundary condition two is S " (x0)=y0″,S″(xn)=yn″；
Boundary condition three is that assumed function y=f (x) is periodic function using b-a as the period, it is desirable that S (x) is also periodic function, I.e.：
In each subinterval [xn-1,xn], because it is an order polynomial that S (x), which is cubic polynomial, S " (x), it is assumed that node xi Locate S " (xi)=Mi, i=0,1,2 ..., n, then in [xn-1,xn] on：
Twice to above formula integral：
Wherein, CiAnd DiValue be respectively arbitrary constant, acquired by endpoint value, MiUsing spline function in node xiLocate first derivative It is continuous to determine.
4. drilling failure relative risk appraisal procedure according to claim 1, which is characterized in that the density function in step 3 is bent The specific acquisition process of the integrated value of line is：
Design integrating range [a, b] is divided into n equal portions, step-lengthChoose Equidistant Nodes xkThe interpolation type that=a+kh is constructed Quadrature formula is：
In formula,For cotes coefficients, x=a+th is enabled, is had：
As n=2, had by above formula：
It is by upper formula complexification：
It is rewritten as：
CN201810647835.4A 2018-06-22 2018-06-22 A kind of drilling failure relative risk appraisal procedure Pending CN108830491A (en)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104700151A (en) * 2014-05-26 2015-06-10 国网辽宁省电力有限公司 Wind power assessment method based on cubic spline interpolation curve-fitting
CN105022858A (en) * 2015-05-08 2015-11-04 北京航天自动控制研究所 Method of determining boundary of drag acceleration corridor of glide vehicle
CN105243502A (en) * 2015-10-19 2016-01-13 华中科技大学 Hydropower station scheduling risk assessment method and system based on runoff interval prediction
CN106295869A (en) * 2016-08-04 2017-01-04 辽宁工程技术大学 A kind of based on the building settlement Forecasting Methodology improving unbiased function

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104700151A (en) * 2014-05-26 2015-06-10 国网辽宁省电力有限公司 Wind power assessment method based on cubic spline interpolation curve-fitting
CN105022858A (en) * 2015-05-08 2015-11-04 北京航天自动控制研究所 Method of determining boundary of drag acceleration corridor of glide vehicle
CN105243502A (en) * 2015-10-19 2016-01-13 华中科技大学 Hydropower station scheduling risk assessment method and system based on runoff interval prediction
CN106295869A (en) * 2016-08-04 2017-01-04 辽宁工程技术大学 A kind of based on the building settlement Forecasting Methodology improving unbiased function

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
UNDD8EE3: "数值分析62牛顿-柯斯特公式", 《豆丁网》 *
欢乐鸟: "数值分析（样条插值）", 《道客巴巴》 *
沈建文等: "川西深井漏涌卡钻井事故风险识别分析", 《钻采工艺》 *
许小勇等: "基于三次样条插值的列表函数的数值微 分与积分", 《东莞理工学院学报》 *

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Application publication date: 20181116