CN109858147B - Reliability theory-based quantitative evaluation method for borehole wall instability risk - Google Patents
Reliability theory-based quantitative evaluation method for borehole wall instability risk Download PDFInfo
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Abstract
The invention discloses a quantitative evaluation method for borehole wall instability risk based on a reliability theory, which comprises the following steps: s1, according to the basic data of the drilled stratum; s2, according to the input parameter uncertain statistic table established in the step S1; s3, establishing a borehole wall collapse and borehole wall fracture instability limit state model; s4, respectively solving a borehole wall collapse pressure value and a borehole wall rupture pressure value which are limited by basic random variables according to the borehole wall instability limit state model in the step S3; s5, setting a mean value and a coefficient of variation of the wellbore pressure, and generating the wellbore pressure value under the mean value and the coefficient of variation by adopting Monte Carlo simulation; and S6, counting the calculation results to obtain the quantitative evaluation result of the risk of borehole wall collapse and collapse instability. The invention has the beneficial effects that: the method can quantitatively evaluate the borehole wall instability risk under the influence of parameter uncertainty, and can provide more accurate and effective decision basis for drilling technicians and constructors.
Description
Technical Field
The invention relates to the technical field of well wall stability evaluation in petroleum drilling, in particular to a quantitative evaluation method for borehole wall instability risk based on a reliability theory.
Background
At present, unconventional oil and gas resources such as compact oil and gas, coal bed gas, shale oil and gas, ocean deep water oil and gas and the like are gradually paid attention with the exhaustion of the conventional oil and gas resources. In order to effectively develop such unconventional oil and gas resources, more and more inclined wells such as directional wells, horizontal wells, extended reach wells and the like are widely adopted. For example, the large displacement well is adopted to develop beach oil gas, so that the construction of an ocean drilling platform can be avoided; the directional well is adopted to develop ocean oil gas, so that the number of required drilling platforms can be reduced; the horizontal well is adopted to develop compact oil gas, coal bed gas and shale oil gas, so that the drainage area of the contact between a shaft and a reservoir can be effectively increased, the staged fracturing transformation is facilitated, and the oil gas recovery rate is finally improved. However, such deviated well drilling with relatively complex structure has many challenges, such as high risk of borehole instability, high drill string friction/torque, difficult well cleaning, difficult casing running, poor cementing quality due to casing eccentricity, severe casing wear, etc., which result in increased drilling nonproductive time, drilling cycle time, and drilling costs. The borehole wall instability problem is one of focus problems concerned by drilling engineering, usually represents borehole wall collapse and borehole leakage, and accurately controls the pressure of a borehole to be higher than the collapse pressure and lower than the fracture pressure, so that borehole wall instability accidents can be effectively avoided, and underground complications and accidents such as blowout, leakage, collapse and sticking caused by induction can be avoided.
At present, scholars at home and abroad develop deeper research aiming at the problem of well wall stability, establish various empirical models, analytical models and numerical simulation methods, and the focus of the research is mainly focused on constitutive models and destruction criteria. Various models such as a linear elastic analytic solution, a plastic model, an elastoplastic model, a pore elastic model, a pore thermoelastic model, a chemical pore elastic model and a chemical pore thermoelastic model are formed in the aspect of the constitutive model, and various criteria such as a Mohr-Coulomb criterion, a Drucker-Prager criterion, a Mogi-Coulomb criterion, a modified Lade criterion, a modified Wiebols-Cook criterion and a Hoek-Brown criterion are formed in the aspect of the destruction criterion. However,
because of the concealment and uncertainty of the geological conditions of the deep stratum and certain errors of the geophysical well logging and the interpretation method thereof, the geological mechanical parameters (ground stress, pore pressure), rock mechanical parameters and the like of the stratum present strong uncertainty, and accurate input parameters are difficult to determine when borehole wall stability analysis is carried out; if certain deviation occurs in the input parameters, the deviation of the well wall stability analysis result is caused, and even serious errors may occur. Foreign scholars' studies have shown that the input parameters have extremely strong uncertainties and have a very significant effect on borehole wall stability. The reliability theory is one of the most important basic theories for reliability research, and is mainly used for researching mathematical methods and mathematical models for solving various reliability problems and researching quantitative rules of reliability.
In chinese patent, publication No. CN105740583A discloses a well wall stability logging evaluation method suitable for carbonate rock formation, which includes the following steps: and obtaining stratum pore pressure by using an effective stress theorem, establishing a stratum collapse prediction model by using logging information, and obtaining the stratum collapse pressure equivalent mud density by combining the stratum pore pressure so as to obtain a mud density safety range. However, the technical scheme can only solve the problems that the existing traditional evaluation method is narrow in adaptability and insufficient in solving all borehole wall instability. Therefore, the borehole wall instability risk under the influence of parameter uncertainty can be quantitatively evaluated according to the dependence theory, and a more accurate and effective decision basis can be provided for drilling technicians and constructors.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a quantitative evaluation method for borehole wall instability risks under the influence of uncertainty of parameters, which can provide more accurate and effective decision bases for drilling technicians and constructors and is based on a reliability theory.
The purpose of the invention is realized by the following technical scheme: a borehole wall instability risk quantitative evaluation method based on a reliability theory comprises the following steps:
s1, constructing an uncertain statistical table of input parameters according to basic data of the drilled stratum, wherein the input parameters comprise vertical stress, maximum horizontal ground stress, minimum horizontal ground stress, porosity, Poisson' S ratio, cohesion, internal friction angle, well inclination azimuth angle, Biot coefficient, permeability coefficient and mean value and variation coefficient of collapse width parameters;
s2, generating each basic random variable by adopting a Monte Carlo method according to the input parameter uncertain statistical table established in the step S1, wherein the basic random variables comprise vertical stress, maximum horizontal ground stress, minimum horizontal ground stress, porosity, Poisson ratio, cohesion, internal friction angle and Biot coefficient, and any distribution function of uniform distribution, triangular distribution, normal distribution, lognormal distribution, Betay distribution, Bevan distribution, Weibull distribution and gamma distribution is selected according to actual conditions;
s3, establishing a borehole wall collapse and borehole wall fracture instability limit state model according to the basic random variables generated through the distribution function in the step S2;
s4, respectively solving a borehole wall collapse pressure value and a borehole wall rupture pressure value which are limited by basic random variables according to the borehole wall instability limit state model in the step S3;
s5, setting a mean value and a coefficient of variation of the well bore pressure, and generating the well bore pressure value under the mean value and the coefficient of variation by adopting Monte Carlo simulation;
and S6, counting the calculation results according to the borehole wall collapse pressure value, the borehole wall fracture pressure value and the borehole pressure value obtained in the steps S4 and S5 to obtain the quantitative evaluation result of the risk of borehole wall collapse and fracture instability.
The invention has the following advantages: the method solves the problem that the influence of parameter uncertainty cannot be considered in the prior art, the influence possibly caused by input parameters and construction parameter uncertainty cannot be evaluated by the conventional borehole wall stability analysis method, the borehole wall instability risk under the influence of parameter uncertainty can be quantitatively evaluated by the reliability theory, and more accurate and effective decision basis can be provided for drilling technicians and constructors.
Drawings
FIG. 1 is a flow chart of the calculation of the present invention;
FIG. 2 is a graph of instability probability versus reliability;
FIG. 3a is a schematic diagram of coordinate transformation of a wall of an inclined shaft;
FIG. 3b is a schematic view of a periwell destabilization zone;
FIG. 4 is a statistical histogram of vertical stress simulation results;
FIG. 5 is a statistical histogram of maximum horizontal ground stress simulation results;
FIG. 6 is a statistical histogram of rock cohesion simulation results;
FIG. 7 is a statistical histogram of the simulation results of the internal friction angle of the rock;
FIG. 8 is a graph of vertical well borehole wall collapse and fracture probability density functions and cumulative reliability interferograms;
FIG. 9 is a graph of probability density functions and cumulative reliability interferograms for borehole collapse and fracture in an inclined shaft;
FIG. 10 is a horizontal well borehole wall collapse and rupture probability density function and an accumulative reliability interferogram;
FIG. 11 is a graph comparing the results of three well types.
Detailed Description
The invention will be further described with reference to the accompanying drawings, without limiting the scope of the invention to the following:
as shown in FIG. 1, a method for quantitatively evaluating borehole wall instability risk based on reliability theory comprises the following steps:
s1, constructing an uncertain statistical table of input parameters according to basic data of the drilled stratum, wherein the input parameters comprise vertical stress, maximum horizontal ground stress, minimum horizontal ground stress, porosity, Poisson' S ratio, cohesion, internal friction angle, well inclination azimuth angle, Biot coefficient, permeability coefficient and mean value and variation coefficient of collapse width parameters;
s2, generating each basic random variable by adopting a Monte Carlo method according to the input parameter uncertain statistic table established in the step S1, wherein the basic random variables comprise vertical stress, maximum horizontal ground stress, minimum horizontal ground stress, porosity, Poisson ratio, cohesion, internal friction angle and Biot coefficient, and any distribution function of uniform distribution, triangular distribution, normal distribution, lognormal distribution, beta distribution, Gunn Bell distribution, Weibull distribution and gamma distribution is selected according to actual conditions;
s3, establishing a borehole wall collapse and borehole wall fracture instability limit state model according to the basic random variables generated by the distribution function in the step S2;
the method for deducing the borehole wall instability limit state model comprises the following steps:
(1) theory of reliability
According to the reliability theory, the factors influencing borehole wall instability can be divided into two types of comprehensive quantity, namely a load random variable QkAnd resistance random variable RkWhere k may take C and F, representing borehole wall collapse and borehole wall fracture, respectively. Random variable Q of order loadkAnd resistance random variable RkRespectively as follows:
wherein Q iskIs a load random variable; rkIs a resistance random variable; k is a subscript of collapse instability and rupture instability, and C and F can be taken; xRkiIs a load random variable element; xSkiIs a resistance random variable element; i is a subscript of the number of random variable elements, i is 1,2, …, n; n is the total number of random variable elements.
The functional function of borehole wall instability can therefore be expressed as:
Zk＝g(Qk,Rk)＝Rk-Qk-----------------------------------(2)
wherein, ZkIs a function; g is a function.
Z may occur due to differences in external loads and wellbore pressuresk>0、Zk＝0、Zk<And 0, three cases. According to ZkThe pressure of the shaft can be judged whether to meet the functional requirement of stabilizing the shaft wall, so the formula (2) can be called as a functional function, and the ultimate equilibrium state of the functional function is the basis for evaluating the reliability and can be expressed as follows:
Zk＝g(Qk,Rk)＝0--------------------------------------------(3)
due to the random variation Q of the loadkSum resistance random variable RkAre all affected by basic random variables such as ground stress, pore pressure, rock strength, wellbore pressure, etc., where the basic random variable for borehole wall instability is assumed to be (X)k1,Xk2,…,Xkn) Then its function can be further expressed as:
Zk＝g(Xk1,Xk2,…,Xkn)---------------------------------------(4)
wherein, XknIs a basic random variable element; n is the total number of random variable elements;
according to the reliability theory, the reliability index can be expressed as:
wherein, betakIs a reliability index; μ (x) is the random variable x mean; σ (x) is the standard deviation of the random variable x.
In general, the probability that the function is in the instability state is referred to as instability probability, and if the function conforms to normal distribution, the instability probability and reliability corresponding to borehole wall collapse and borehole wall fracture can be expressed as follows:
wherein, PfkIs the destabilization probability; prkReliability is obtained; Φ is the standard normal distribution function.
The reliability and the instability probability have the following relationship:
Prk+Pfk＝1--------------------------(7)
fig. 2 is a schematic diagram of obtaining the instability probability and the reliability through the probability density, in the diagram, the area obtained by accumulating the blue region probability density with the pressure less than 0 is the instability probability, the area obtained by accumulating the red region probability density with the pressure greater than 0 is the reliability, and the intersection point of the accumulated probability curve and the longitudinal coordinate with the pressure of 0 is the instability probability. Therefore, the larger the area where the pressure is less than 0, the lower the reliability; the smaller the area where the pressure is less than 0, the higher the reliability. According to the reliability theory, the quantitative evaluation of the borehole wall instability risk can be realized by calculating the occurrence probability of the instability region.
(2) Stress distribution model for inclined shaft well wall
Considering deep formation rock as a uniform, continuous, isotropic elastic medium, fig. 3a, a borehole wall stress distribution model is obtained by taking a radial distance R ═ R according to a borehole stress elastic solution given by Bradley (1979):
wherein:
wherein σr,σθ,σz,τθzIs the borehole wall stress component, MPa; a, B, C, D, E, F, G, H and J are coordinate transformation coefficients without dimension; sigmav,σH,σhVertical, maximum and minimum horizontal ground stress, MPa, respectively; p is a radical of formulamThe drilling fluid column pressure is MPa; delta is a permeability coefficient, wherein delta is 0 when the well wall is impermeable, and delta is 1 when the well wall is permeable; θ is the well angle, (°); i is the angle of the well, (°); alpha is the included angle between the well deviation direction and the maximum horizontal ground stress direction (degree); ν is the poisson ratio; k1The seepage effect coefficient and decimal number; phi is porosity,%; alpha is alphapIs the Biot coefficient; p is a radical ofpPore pressure, MPa.
Because the radial stress is a main stress, and the other two main stresses are positioned in a theta z tangent plane of the well wall, the three main stresses of the well wall can be solved according to the theory of mechanics of materials:
wherein σi,σj,σkThree main stresses are the well wall, MPa.
Sequencing the three main stresses to obtain the maximum and minimum main stresses of the well wall, combining the strength criterion to obtain the nonlinear equation of the collapse pressure and the fracture pressure required by solving the stable well wall, solving the equation to obtain the collapse pressure and the fracture pressure, and further converting to obtain the equivalent density of the collapse pressure and the equivalent density of the fracture pressure.
(3) Criterion of rock destruction
For borehole wall shear failure, the most common criterion for borehole wall stability analysis is the Mohr-Coulomb criterion, which can be expressed as:
wherein σ1,σ2,σ3Maximum, intermediate and minimum principal stress, MPa, respectively; c-cohesion, MPa;
internal angle of friction, (°).
For conditions under which tensile failure occurs, depending primarily on the formation rock tensile strength, the tensile failure criterion can be expressed as: sigma3-αppp+St＝0--------------------------------------------------(12)
Wherein S istThe tensile strength of rock is MPa.
(4) Extreme state model for borehole wall collapse instability
The minimum wellbore pressure required to maintain borehole wall stability may be defined as the collapse pressure, and in the typical case, the borehole wall radial stress will be the minimum principal stress (σ)3＝σi) And is shown by the formula (10)σj>σk. Therefore, will σ1＝σjAnd σ3＝σiThe collapse pressure nonlinear equation can be derived from equation (11):
wherein p isCCollapse pressure, MPa; f. ofCAs a function of collapse pressure;
function fCThe physical meaning of (A) is clear: the ability of the formation rock to resist borehole wall shear stress. If fC<0, shear failure will occur; if f isCWhen the value is 0, the limit balance is achieved; if fC>0, no shear failure occurs. In general, in order to solve equation (13), it is necessary to determine the critical point at which the stress concentration is the most severe, as shown in fig. 3b, that is, the point a with the highest stress in the graph, and the corresponding well circumferential angle θ ═ θmax. However, considering that the actual borehole allows a certain degree of breakout, the breakout width model proposed by Zoback (2007) is used here, as shown in fig. 3B, the breakout width is 2 ω, the borehole wall instability critical point at this time is point B, and the corresponding borehole circumferential angle is:
θ＝θmax±ω-------------------------------------------------(14)
wherein, thetamaxThe well circumferential angle (DEG) corresponding to the highest stress concentration point of the well wall; ω is the breakout width parameter, (°).
Changing theta to thetamaxAfter + -omega is brought into the formula (9), the borehole wall collapse pressure is solved according to the formula (13), and the collapse pressure under the condition of allowing a certain collapse width (2 omega) can be obtained.
When the pressure of the well bore is lower than the collapse pressure, namely the collapse instability of the well wall occurs, the stress concentration of the stratum around the well is caused to be a load causing the collapse instability of the well wall, and the pressure of the well bore is a resistance force for supporting the stability of the well wall. Considering the factors influencing the collapse of the well wall including the earth stress, the pore pressure, the mechanical parameters of the stratum rocks, the well track, the collapse width and the like, the load random variable Q of the well wall collapse is consideredCAnd resistance random variable RCCan be respectively expressed as:
therefore, the reliability index, the instability probability and the reliability corresponding to the extreme state of borehole wall collapse and instability are respectively as follows:
(5) extreme state model for borehole wall fracture instability
The highest wellbore pressure that prevents the wellbore wall from being fractured may be defined as the fracture pressure. From the formula (10), σiAnd σjGreater than zero, only σkNegative values may occur. Therefore, will σ3＝σkThe break pressure nonlinear equation can be derived from equation (12):
fF(pF)＝σk-αppp+St＝0-------------------------------------------(18)
wherein p isFRupture pressure, MPa; f. ofFAs a function of the burst pressure.
Function fFThe physical meaning of (A) is clear: the ability of the formation rock to resist borehole wall tensile stress. If f isF<0, tensile failure will occur; if fFWhen the value is 0, the limit balance is achieved; if fF>0, no tension failure occurs.
Similarly, when the wellbore pressure is higher than the fracture pressure, i.e., borehole wall fracture instability occurs, the wellbore pressure becomes a load causing the borehole wall to fracture, and the surrounding formation environment becomes a resistive force against the borehole wall fracture. Considering the factors influencing the well wall fracture including the earth stress, the pore pressure, the mechanical parameters of the stratum rocks, the well track and the like, the load of the well wall fracture is randomly changedQuantity QFAnd resistance random variable RFCan be respectively expressed as:
therefore, the reliability index, the instability probability and the reliability corresponding to the borehole wall fracture instability limit state are respectively as follows:
s4, respectively solving a borehole wall collapse pressure value and a borehole wall rupture pressure value which are limited by basic random variables according to the borehole wall instability limit state model in the step S3;
s5, setting a mean value and a coefficient of variation of the wellbore pressure, and generating the wellbore pressure value under the mean value and the coefficient of variation by adopting Monte-Carlo simulation;
and S6, counting the calculation results according to the borehole wall collapse pressure value, the borehole wall fracture pressure value and the borehole pressure value obtained in the steps S4 and S5 to obtain the quantitative evaluation result of the risk of borehole wall collapse and fracture instability.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
Analyzing by taking a CW-101X well beard river set stratum of an oil field of the Sichuan basin as an example, wherein the burial depth of the beard river set stratum is 2500-3500 m, according to the logging and actual drilling data of the drilled beard river set stratum, the stratum has a vertical stress of 52.10-69.52MPa, a maximum horizontal ground stress of 42.55-59.47 MPa (N37.86 DEG E), a minimum horizontal stress of 35.63-49.68 MPa, a pore pressure of 26.95-33.24, a rock cohesion of 12.15-18.63 MPa, an internal friction angle of 33.54-36.67 degrees, a rock tensile strength of 3.47-5.63 MPa, a rock Poisson ratio of 0.23-0.27 and a porosity of 0.05-0.16, and an uncertain input parameter statistical table is constructed through statistical analysis, the input parameters include vertical stress, maximum horizontal ground stress, minimum horizontal ground stress, porosity, poisson's ratio, cohesion, internal friction angle, well deviation azimuth angle, Biot coefficient, permeability coefficient, and mean and variation coefficient statistics of breakout width parameters are shown in the following table:
| No. | random variable | Mean value | Standard deviation of | Coefficient of | P10 | P90 | |
| 1 | Vertical stress/MPa | 57.82 | 2.89 | 0.05 | 53.22 | 62.42 | |
| 2 | Maximum horizontal ground stress/MPa | 50.05 | 10.01 | 0.20 | 34.12 | 65.98 | |
| 3 | Horizontal minimum ground stress/MPa | 41.63 | 2.08 | 0.05 | 38.32 | 44.94 | |
| 4 | Horizontal maximum stress azimuth/(°) | 37.86 | 7.57 | 0.20 | 25.81 | 49.91 | |
| 5 | Pore pressure/MPa | 29.50 | 8.85 | 0.30 | 15.42 | 43.58 | |
| 6 | cohesion/MPa | 16.47 | 6.59 | 0.40 | 5.98 | 26.96 | |
| 7 | Internal angle of friction/(°) | 34.67 | 6.93 | 0.20 | 23.64 | 45.70 | |
| 8 | Tensile strength/MPa | 3.85 | 1.54 | 0.40 | 1.40 | 6.30 | |
| 9 | Poisson ratio | 0.25 | 0.05 | 0.20 | 0.17 | 0.33 | |
| 10 | Porosity of | 0.10 | 0.02 | 0.20 | 0.07 | 0.13 |
Wherein: p10 and P90 correspond to the upper and lower confidence limits of the confidence interval at 90% confidence level respectively
And generating each basic random variable by adopting a Monte-Carlo method according to the input parameter uncertain statistic table established in the step S1. Generally, geomechanical parameters and rock mechanical parameters related to borehole wall stability analysis are uncertain, and mathematical methods for describing parameter uncertainty in reliability theory include uniform distribution, triangular distribution, normal distribution, lognormal distribution, Beta distribution, Gumbel distribution, Weibull distribution, Gamma distribution and the like, and the most commonly used methods are normal distribution, lognormal distribution and Weibull distribution. Assuming that geomechanical parameters and rock mechanical parameters of the wujia river group stratum basically meet normal distribution, setting the mean value of each parameter according to the well logging interpretation result, and setting the variation coefficient and the standard deviation of each parameter by calculating the possible error range of the related parameters according to various testing methods on site. The Monte-Carlo method is adopted for simulation to carry out random sampling simulation on input parameters, the number of random sampling simulation samples is 10000, and statistical results and normal distribution fitting curves of part of parameter simulation are shown in figures 4-7. As can be seen from the graph, the uncertain distribution rule of each parameter satisfies the normal distribution rule; the higher the coefficient of variation, the stronger the uncertainty of the sample data; and vice versa. For example, the coefficient of variation of the cohesive force of the rock reaches 0.40, and the confidence interval corresponding to 90% of confidence coefficient is 5.98-26.96 MPa; the variation coefficient of the vertical stress is 0.05, and the confidence interval corresponding to 90% confidence coefficient is 53.22-62.42 MPa; in contrast, the lower the coefficient of variation, the lower the confidence interval, i.e., the more concentrated the sample data, the weaker the uncertainty. It follows that this relatively strong uncertainty in the parameters will tend to have a significant effect on borehole wall stability.
Further, according to the basic random variables generated in the step S2, a borehole wall collapse and borehole wall fracture instability limit state model is established; respectively solving a borehole wall collapse pressure value and a borehole wall fracture pressure value which are limited by basic random variables according to the borehole wall instability extreme state model in the step S3; giving a shaft pressure mean value and a variation coefficient, and generating a shaft pressure value under the given mean value and the variation coefficient by adopting Monte-Carlo simulation; and evaluating the risk of borehole wall collapse and collapse instability according to the borehole wall collapse pressure value, the borehole wall collapse pressure value and the borehole pressure value obtained in the steps S4 and S5, and counting the calculation result to obtain the quantitative evaluation result of the risk of borehole wall collapse and collapse instability. In order to reveal the comprehensive risk of borehole wall instability under different borehole types, borehole wall collapse and collapse instability risks under three types of typical borehole types, namely a vertical borehole, an inclined borehole (azimuth 45 degrees and borehole inclination 45 degrees) and a horizontal borehole (azimuth 45 degrees and borehole inclination 90 degrees) are analyzed, the results are shown in figures 8-11, the probability density functions of borehole wall collapse and fracture and the cumulative reliability interference graphs under the three types of typical borehole types are respectively shown in figures 8-10, and the comparison graphs of the reliability of the three types of typical borehole types are shown in figure 11.
(1) In the interference graph of the probability density function of borehole wall collapse and collapse, the overlapping part of the probability density of borehole wall collapse and the probability density of borehole wall collapse is called an interference area, and the interference area is an area where collapse and collapse instability can occur simultaneously: the larger the area of the interference region is, the lower the reliability of successful drilling is; the smaller the area of the interference zone, the higher the reliability of successful drilling.
(2) In the cumulative reliability interferogram of borehole wall collapse and collapse instability, the left side of the collapse reliability curve is a collapse instability risk area, the right side of the collapse reliability curve is a collapse instability risk area, and meanwhile, an area for avoiding borehole wall collapse and collapse instability (namely, an area contained in the lower part of the borehole wall collapse reliability curve and the borehole wall collapse reliability curve) represents a safe area capable of being successfully drilled.
(3) For three typical well types, the safety windows of a vertical well, an inclined well and a horizontal well under the condition of 95% of reliability are respectively 1.19-1.98 g/cm3、1.36～2.18g/cm3And 1.47 to 2.19g/cm3The safe density window with a wider and reliable window is formed in the direction no matter whether the vertical well, the inclined well or the horizontal well is drilled; if the borehole wall stability reliability is reduced to 90% or lower, the corresponding safety window will be wider, but the risk of borehole wall instability will also be significantly increased; in comparison, if the same wellbore pressure is adopted, the risk of collapse and instability of a vertical well is lower, and the risk of a horizontal well is higher in the second time of an inclined well, which is consistent with the collapse pressure distribution trend obtained by adopting mean value calculation.
(4) The borehole wall instability risk evaluation result obtained based on the reliability theory is still consistent with the conventional borehole wall stability analysis result in the overall trend, however, the influence possibly caused by the uncertainty of input parameters and construction parameters cannot be evaluated by the conventional borehole wall stability analysis method, the borehole wall instability risk under the influence of the uncertainty of the parameters can be quantitatively evaluated by the reliability theory, and more accurate and effective decision-making basis can be provided for drilling technicians and constructors.
In conclusion, the method solves the problem that the influence of uncertainty of parameters cannot be considered in the prior art, the influence possibly caused by uncertainty of input parameters and construction parameters cannot be evaluated by a conventional borehole wall stability analysis method, the borehole wall instability risk under the influence of uncertainty of parameters can be quantitatively evaluated by a reliability theory, and more accurate and effective decision basis can be provided for drilling technicians and constructors.
Claims (1)
1. A quantitative evaluation method for borehole wall instability risk based on a reliability theory is characterized by comprising the following steps: it comprises the following steps:
s1, constructing an uncertain statistical table of input parameters according to basic data of the drilled stratum, wherein the input parameters comprise vertical stress, maximum horizontal ground stress, minimum horizontal ground stress, porosity, Poisson' S ratio, cohesion, internal friction angle, well inclination azimuth angle, Biot coefficient, permeability coefficient and mean value and variation coefficient of collapse width parameters;
s2, generating each basic random variable by adopting a Monte Carlo method according to the input parameter uncertain statistical table established in the step S1, wherein the basic random variables comprise vertical stress, maximum horizontal ground stress, minimum horizontal ground stress, porosity, Poisson ratio, cohesion, internal friction angle and Biot coefficient, and any distribution function of uniform distribution, triangular distribution, normal distribution, lognormal distribution, Betay distribution, Bevan distribution, Weibull distribution and gamma distribution is selected according to actual conditions;
s3, establishing a borehole wall collapse and borehole wall fracture instability limit state model according to the basic random variables generated through the distribution function in the step S2;
s4, respectively solving a borehole wall collapse pressure value and a borehole wall fracture pressure value which are limited by basic random variables according to the borehole wall instability limit state model in the step S3;
s5, setting a mean value and a coefficient of variation of the well bore pressure, and generating the well bore pressure value under the mean value and the coefficient of variation by adopting Monte Carlo simulation;
s6, according to the borehole wall collapse pressure value, the borehole wall fracture pressure value and the borehole pressure value obtained in the steps S4 and S5, calculating results to obtain quantitative evaluation results of the borehole wall collapse and fracture instability risks;
the construction steps of the borehole wall instability limit state model are as follows:
(1) theory of reliability
According to the reliability theory, the factors influencing borehole wall instability can be divided into two types of comprehensive quantity, namely a load random variable QkSum resistance random variable RkWherein k can be C and F, which respectively represent two conditions of borehole wall collapse and borehole wall rupture; random variable Q if order loadkAnd resistance random variable RkRespectively as follows:
wherein Q iskIs a load random variable; rkIs a resistance random variable; k is a subscript of collapse instability and collapse instability, and C and F can be taken; xRkiIs a load random variable element; xSkiIs a resistance random variable element; i is a subscript of the number of random variable elements, i is 1,2, …, n; n is the total number of random variable elements;
the functional function of borehole wall instability can therefore be expressed as:
Zk＝g(Qk，Rk)＝Rk-Qk
wherein, ZkIs a function; g is a function;
according to the reliability theory, the quantitative evaluation of the borehole wall instability risk can be realized by calculating the occurrence probability of the instability region;
(2) inclined shaft wall stress distribution model
Taking deep stratum rock as a uniform, continuous and isotropic elastic medium, and obtaining a borehole wall stress distribution model by taking a radial distance R as R according to a borehole stress elastic solution given by Bradley; the radial stress is a main stress, the other two main stresses are positioned in a theta z tangent plane of the well wall, and three main stresses of the well wall can be solved according to the theory of mechanics of materials:
wherein σi,σj,σkThree main stresses are well wall, MPa; sigmar，σθθ，σzz，τθzIs a borehole wall stress component, MPa; p is a radical of formulamThe drilling fluid column pressure is MPa; delta is a permeability coefficient, wherein delta is 0 when the well wall is impermeable, and delta is 1 when the well wall is permeable; theta is the well circumference angle, °; i is the inclination angle; phi is porosity,%; p is a radical of formulapPore pressure, MPa;
sequencing the three main stresses to obtain the maximum and minimum main stresses of the well wall, combining with a strength criterion to obtain a non-linear equation of the collapse pressure and the fracture pressure required by solving the stable well wall, solving the equation to obtain the collapse pressure and the fracture pressure, and further converting to obtain the equivalent density of the collapse pressure and the equivalent density of the fracture pressure;
(3) criterion of rock failure
For borehole wall shear failure, the most common criterion for borehole wall stability analysis is the Mohr-Coulomb criterion, which can be expressed as:
wherein σ1,σ2,σ3-maximum, intermediate and minimum principal stresses, MPa, respectively; c-cohesion, MPa;
-internal friction angle, °; alpha is alphapIs the Biot coefficient; p is a radical of formulapPore pressure, MPa;
for conditions under which tensile failure occurs, depending primarily on the formation rock tensile strength, the tensile failure criterion can be expressed as:
σ3-αppp+St＝0
wherein S istRock tensile strength, MPa;
(4) extreme state model for borehole wall collapse instability
The minimum wellbore pressure required to maintain borehole wall stability may be defined as the collapse pressure, and the borehole wall radial stress will be the minimum principal stress, σ3＝σiAnd σ is known from the principal stress equationj>σkThus, will σ1＝σjAnd σ3＝σiThe collapse pressure nonlinear equation can be obtained by substituting the effective stress equation:
wherein p isCCollapse pressure, MPa; f. ofCAs a function of collapse pressure;
(5) extreme state model for borehole wall fracture instability
The highest wellbore pressure that prevents the wellbore wall from being fractured may be defined as the fracture pressure; will sigma3＝σkThe breaking pressure nonlinear equation can be obtained by substituting the tension failure criterion formula: f. ofF(pF)＝σk-αppp+St＝0
Wherein p isFBurst pressure, MPa; f. ofFAs a function of the burst pressure;
when the pressure of the well bore is higher than the fracture pressure, namely the fracture instability of the well wall occurs, the pressure of the well bore becomes the load causing the fracture of the well wall, and the formation environment around the well becomes the resistance resisting the fracture of the well wall; random variable Q of load of well wall fractureFAnd resistance random variable RFCan be represented as:
wherein σv,σH,σhVertical, maximum and minimum horizontal ground stress, MPa, respectively; p is a radical ofmThe drilling fluid column pressure is MPa; delta is a permeability coefficient, delta is 0 when the well wall is impermeable, and delta is 1 when the well wall is permeable; i is the angle of inclination, degree; alpha is the included angle between the well inclination direction and the maximum horizontal ground stress direction; v is the Poisson's ratio; phi is porosity,%; c-cohesion, MPa;
-internal friction angle, °; alpha is alphapIs the Biot coefficient; p is a radical ofpPore pressure, MPa;
the reliability index, the instability probability and the reliability corresponding to the extreme state of the well wall fracture instability are respectively as follows:
wherein beta isF、PfF、PrFRespectively corresponding reliability index, instability probability and reliability of the borehole wall fracture instability limit state; phi is a standard normal distribution function; mu is the mean value of random variables; sigma is a standard deviation of random variables; z is a linear or branched memberFA function representing borehole wall fracture.
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