CN112347424B - Evaluation method for ultra-temperature high-pressure development safety drilling probability based on Weibull function - Google Patents
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Abstract
The invention discloses an evaluation method of ultra-temperature high-pressure development safety drilling probability based on Weibull function. The method comprises the following steps: collecting a pore pressure data sample of the ultra-high temperature and high pressure stratum and a vertical well fracture pressure data sample; obtaining probability density distribution of the pore pressure of each section and the fracture pressure of the vertical well according to the occurrence frequency of the pore pressure of each section and the fracture pressure of the vertical well; determining a pore pressure and vertical well fracture pressure probability density double-parameter Weibull function expression; integrating to obtain a cumulative probability function expression of pore pressure and vertical well fracture pressure; determining an accumulated probability expression of the safety pressure of the vertical well; determining a cumulative probability expression of the safety pressure of the directional well; and calculating the safe drilling probability value of the ultra-high temperature and high pressure directional well. The method can evaluate the safety drilling probability before the development of the well drilling, avoid high-risk operation, reduce cost and safety accidents, and has important significance for the development of the high-temperature high-pressure oil-gas field.
Description
Technical Field
The invention relates to an evaluation method of ultra-temperature high-pressure development safety drilling probability based on Weibull function, and belongs to the field of petroleum drilling and production.
Background
The temperature of the deep stratum of the ultra-high temperature high pressure oil-gas field exceeds 180 ℃, the pore pressure coefficient exceeds 2.20, the fracture pressure coefficient of a vertical well is generally lower than 2.42, the pressure window is narrow, the accident rate is high, and the drilling risk is extremely high. In order to ensure safe and economical development of the ultra-high temperature high pressure oil gas field, the safe drilling probability value of a development well (directional well) is quantitatively evaluated in a pre-drilling stage based on the drilled well statistical analysis.
Compared with the normal temperature and pressure and the general high temperature and pressure area, the formation temperature and pressure of the ultra-temperature and high pressure area are higher: 1) Normal temperature and pressure region: the formation temperature is lower than 150 ℃, and the pore pressure coefficient is lower than 1.8; 2) General high temperature and high pressure region: the formation temperature is between 150 ℃ and 180 ℃, and the pore pressure coefficient is between 1.8 and 2.2; 3) Ultra-temperature high-pressure region: the formation temperature exceeds 180 ℃ and the pore pressure coefficient exceeds 2.2. In terms of safe drilling probability assessment, the uncertainty of the existing method on pore pressure and fracture pressure is treated according to the assumption of normal distribution, which is only a qualitative assumption, and actual measurement value samples and probability statistical analysis are not adopted. There is therefore a need for improvements over existing methods.
Disclosure of Invention
The invention aims to provide an evaluation method for the probability of ultra-temperature high-pressure development safety drilling based on Weibull function, which can accurately and quantitatively evaluate the probability of ultra-temperature high-pressure oil and gas field development drilling safety.
The research object focuses on the ultra-temperature high-pressure area, breaks through the limitations of normal temperature and normal pressure and common high-temperature high-pressure areas, overcomes the hypothetical defects of the existing evaluation method, and realizes the safe drilling probability quantitative evaluation of the ultra-temperature high-pressure development well to be drilled from the actual measurement value and probability statistics of the ultra-temperature high-pressure drilled well.
The invention provides an evaluation method of the probability of safe drilling of ultra-temperature and high-pressure development based on Weibull function, which comprises the following steps:
1) Acquiring a pore pressure data sample of the ultra-high temperature and high pressure stratum, and equally dividing the pore pressure data sample into a plurality of interval units from the lowest value to the highest value for statistics to obtain the frequency of occurrence of pore pressure in each interval, thereby obtaining the probability density distribution of the pore pressure in each interval;
2) Acquiring a vertical well fracture pressure data sample, and equally dividing the vertical well fracture pressure data sample into a plurality of interval units from the lowest value to the highest value for statistics to obtain the occurrence frequency of the vertical well fracture pressure in each interval, thereby obtaining the probability density distribution of the vertical well fracture pressure in each interval;
3) Describing a probability density curve of pore pressure and a probability density curve of vertical well fracture pressure by utilizing a double-parameter Weibull function, respectively fitting to obtain shape parameters alpha and alpha 'and scale parameters beta and beta' by utilizing a least square method, and substituting the shape parameters alpha and alpha 'and the scale parameters beta and beta' into a function to obtain a probability density function expression of the pore pressure and a probability density function expression of the vertical well fracture pressure;
4) Integrating the probability density function of the pore pressure and the probability density function of the vertical well fracture pressure respectively to obtain a cumulative probability function expression of the pore pressure and a cumulative probability function expression of the vertical well fracture pressure;
5) Based on the accumulated probability of the vertical well fracture pressure, according to the basic rule of the reciprocal event probability operation, an accumulated probability function expression of the vertical well safety pressure is obtained, wherein the accumulated probability of the vertical well safety pressure represents the accumulated probability that the vertical well does not fracture;
6) Under the actual condition that the directional well is not subjected to fracture pressure test generally, according to the analytic solution of the fracture pressure proportion of the directional well and the vertical well, an accumulated probability function expression of the safety pressure of the directional well is obtained, and the accumulated probability of the safety pressure of the directional well represents the accumulated probability that the directional well is not broken;
7) And according to a probability algorithm, carrying out probability multiplication on the cumulative probability of the pore pressure and the cumulative probability of the directional well safety pressure, and finally obtaining a safety drilling probability value of the ultrahigh-temperature high-pressure directional well, wherein the higher the value is, the lower the drilling risk is.
In the above-mentioned evaluation method, in step 1), the ultra-temperature high-pressure exploratory well is subjected to pressure measurement sampling (MDT) or drill pipe stratum testing (DST), and the pore pressure data sample is obtained from the test result.
In the above evaluation method, in step 2), a floor drain experiment is performed on the ultra-high temperature and high pressure exploratory well, and the vertical well fracture pressure data sample is obtained according to the experimental result and the bottom hole pressure measuring value when the leakage occurs in the drilling process.
In the above evaluation method, in step 3), regression fitting is performed on the dual-parameter Weibull function of the pore pressure and the fracture pressure probability density of the vertical well by a least square method, so as to obtain the shape parameters α, α 'and the scale parameters β, β', respectively, and obtain the dual-parameter Weibull function expression representing the pore pressure and the fracture pressure probability density of the vertical well;
the probability density function expression of the pore pressure is shown as the formula (1):
the probability density function expression of the vertical well fracture pressure is shown as the formula (2):
wherein f (P p ) Represents the probability density of pore pressure, f (P) f ) Represents the probability density, P, of the fracture pressure of the vertical well p Represents pore pressure, P f The method comprises the steps of representing the magnitude of the vertical well fracture pressure, alpha representing the shape parameter of the pore pressure dual-parameter Weibull function, beta representing the scale parameter of the pore pressure dual-parameter Weibull function, alpha 'representing the shape parameter of the vertical well fracture pressure dual-parameter Weibull function, and beta' representing the scale parameter of the vertical well fracture pressure dual-parameter Weibull function.
In the above evaluation method, in step 4), the cumulative probability function expression of the pore pressure is shown in formula (3):
the cumulative probability function expression of the vertical well fracture pressure is shown as the formula (4):
wherein P (P p ) Represents the cumulative probability of pore pressure, P (P f ) Representing the cumulative probability of fracture pressure for a vertical well.
In the above evaluation method, in step 5), the cumulative probability function expression of the vertical well safety pressure is shown in formula (5):
wherein,representing the fracture pressure of the vertical wellSafety) cumulative probability; p (P) f ) Representing the probability of pressure build-up of a vertical well fracture.
In the above evaluation method, in step 6), the cumulative probability function expression of the directional well safety pressure is shown in formula (6):
wherein K represents the ratio of directional well to vertical well fracture pressure.
In the above evaluation method, in step 7), the cumulative probability P (P) of the pore pressure is calculated based on the probability algorithm p ) And cumulative probability of directional well fracture pressure safetyAnd (3) multiplying the two values to finally obtain a safe drilling probability value P (safe) of the ultra-high temperature and high pressure directional well, wherein the higher the safe drilling probability value P is, the lower the drilling risk is.
According to the invention, the safe drilling probability of the ultra-high temperature and high pressure development well is obtained by utilizing the actually measured value samples of the pore pressure and the fracture pressure of the ultra-high temperature and high pressure exploration well based on the double-parameter Weibull probability density function and the probability algorithm, and the higher the probability value is, the lower the drilling risk is.
The invention provides a method for quantitatively evaluating the safe drilling probability of a development well by utilizing measured data samples of the pore pressure and the fracture pressure of a drilled well at high temperature and high pressure. The drilling safety probability can be evaluated before the development of the well drill, the high-risk operation is avoided, the cost and the safety accidents are reduced, and the method has important significance for the development of the ultra-high-temperature high-pressure oil-gas field.
The method provided by the invention has clear and feasible technical route and wide data sources, and can realize the evaluation of the probability of ultra-high temperature and high pressure development safety drilling.
Drawings
FIG. 1 is a flow chart of the evaluation method of the present invention.
FIG. 2 is a probability graph of safe drilling of the directional well at high temperature and high pressure obtained by the method of the invention.
FIG. 3 is a plot of formation pore pressure and cyclic equivalent drilling fluid density probability distribution at 1800m for a vertical well.
FIG. 4 is a graph of probability distribution of formation fracture pressure and cycle equivalent drilling fluid at 1800m for a vertical well.
Detailed Description
The experimental methods used in the following examples are conventional methods unless otherwise specified.
Materials, reagents and the like used in the examples described below are commercially available unless otherwise specified.
The flow chart of the evaluation method for the probability of the safe drilling of the ultra-temperature high-pressure development based on the Weibull function is shown in figure 1, and the evaluation method comprises the following steps:
1) Acquiring a pore pressure data sample of the ultra-temperature high-pressure stratum according to the pressure measurement sampling (MDT) of the ultra-temperature high-pressure exploratory well and the drilling rod stratum test (DST) result;
2) Obtaining a vertical well fracture pressure data sample of the ultra-high temperature and high pressure stratum according to floor drain experimental data carried out by the ultra-high temperature and high pressure exploratory well and a bottom hole pressure measuring value when a leak occurs in the drilling process;
3) Dividing the pore pressure and vertical well fracture pressure data samples obtained in the step 1) and the step 2) into a plurality of interval units from the lowest value to the highest value at equal intervals for statistics to respectively obtain the occurrence frequency of the pore pressure and the vertical well fracture pressure in each interval;
4) Dividing the two frequencies obtained in the step 3) by the total number of samples respectively, and calculating to obtain probability density distribution of pore pressure and vertical well fracture pressure in each section;
5) The two-parameter Weibull function is selected to respectively describe the pore pressure and the probability density of the fracture pressure of the vertical well, the expression is as follows, the shape parameters alpha and alpha 'and the scale parameters beta and beta' in the function are respectively obtained by fitting by using a least square method, and the probability density f (P) of the pore pressure and the fracture pressure of the vertical well is obtained by substituting the shape parameters alpha and alpha 'and the scale parameters beta and beta' into the function p )、f(P f ) A functional expression;
wherein f (P) p ) For the pore pressure probability density, f (P f ) Probability density, P, of fracture pressure for a vertical well p For pore pressure, P f The method comprises the steps that (1) the vertical well fracture pressure is formed, alpha is the shape parameter of the pore pressure double-parameter Weibull function, beta is the scale parameter of the pore pressure double-parameter Weibull function, alpha 'is the shape parameter of the vertical well fracture pressure double-parameter Weibull function, and beta' is the scale parameter of the vertical well fracture pressure double-parameter Weibull function;
6) At the point of the '0's, ++ infinity]Integrating the pore pressure and the probability density function of the vertical well fracture pressure in a range to obtain the cumulative probability P (P) p )、P(P f ) The functional expression is as follows:
wherein P (P) p ) For pore pressure build-up probability, P (P f ) The probability is accumulated for the vertical well fracture pressure.
7) Cumulative probability P (P) based on vertical well fracture pressure f ) Obtaining the cumulative probability of the fracture pressure (safety) of the vertical well according to the basic rule of the reciprocal event probability operationThe functional expression:
in the method, in the process of the invention,representing the safety pressure accumulation probability of the vertical well; p (P) f ) Representing the probability of pressure build-up of a vertical well fracture.
8) Under the realistic condition that the directional well is not generally subjected to fracture pressure test, the cumulative probability function expression of the directional well safety pressure is obtained by analyzing the fracture pressure proportion K of the directional well and the vertical wellWherein the analytical solution expression of K is as follows:
wherein P is f1 ＝3σ H -(σ h cos 2 ψ+σ V sin 2 ψ)-Biot·P p +S t
P f2 ＝3σ h -(σ H cos 2 ψ+σ V sin 2 ψ)-Biot·P p +S t
In sigma H For horizontal maximum ground stress, sigma h For horizontal minimum ground stress, biot is the effective stress coefficient, θ is azimuth, ψ is well inclination, P p Is pore pressure, S t Is the tensile strength of the stratum.
9) Obtaining pore pressure cumulative probability P (P) using step 6) and step 8), respectively p ) And cumulative probability of directional well safety pressureAnd then, carrying out probability multiplication on the two events according to a probability algorithm to finally obtain a safe drilling probability value P (safe) of the ultra-high temperature high pressure directional well, wherein the higher the value is, the lower the drilling risk is.
FIG. 2 is a probability graph of safe drilling of a directional well at high temperature and high pressure, from which it can be seen that the method of the present invention can quantitatively evaluate the magnitudes of the safe drilling probability values of different well deviation development wells, the greater the well deviation angle, the lower the safe drilling probability value; under the condition of fixed well inclination, the drilling fluid density peak value with higher safety probability is positioned on the right side.
The prior method (such as Nanyan, etc. the quantitative evaluation method of drilling engineering risk based on uncertainty analysis [ J ]. The national institute of petroleum, university of China, 2019,43 (02): 91-96 ]) is to perform qualitative judgment through probability density distribution of pore pressure and fracture pressure, such as the probability distribution diagram of formation pore pressure and circulating equivalent drilling fluid density at 1800m of a certain vertical well in FIG. 3, and the probability distribution diagram of formation fracture pressure and circulating equivalent drilling fluid density at 1800m of a certain vertical well in FIG. 4. The "presence or absence of risk" is represented by the "presence or absence of intersection" of the histogram representing formation pore pressure (left side in fig. 3, right side in fig. 4) with the histogram representing fracture pressure (right side in fig. 3, left side in fig. 4), and the result was not truly quantified. It can be seen that the prior art method includes subjective factors-circulating equivalent drilling fluid density, and is not an objective feature of a 100% reactive formation. The prior method divides two risks of pore pressure and fracture pressure, and respectively carries out qualitative judgment, but actually the safe drilling probability is determined by the two risks. The prior method considers that the random variable of the pore pressure meets the normal distribution by supposing, and the actual measurement shows that the pore pressure and the fracture pressure of the ultra-temperature high-pressure area do not meet the normal distribution. The existing method only aims at a common high-temperature high-pressure exploratory well, and does not aim at a development well of the high-temperature high-pressure exploratory well.
The method eliminates the interference of subjective factors and truly reflects the objective characteristics of the stratum. The probability product method is adopted to integrate the pore pressure and the fracture pressure, so that the safety probability value of the ultra-high temperature high pressure directional well can be quantitatively obtained, and the method is suitable for directional development wells.
The foregoing description of the exemplary embodiments of the invention is not intended to limit the scope of the invention, but rather to limit the scope of the invention. Moreover, it should be noted that the components of the present invention are not limited to the above-mentioned overall application, and each technical feature described in the specification of the present invention may be selected to be used alone or in combination according to actual needs, so that other combinations and specific applications related to the present invention are naturally covered by the present invention.
Claims (5)
1. An evaluation method of safe drilling probability of ultra-temperature high-pressure development based on Weibull function comprises the following steps:
1) Acquiring a pore pressure data sample of the ultra-high temperature and high pressure stratum, and equally dividing the pore pressure data sample into a plurality of interval units from the lowest value to the highest value for statistics to obtain the frequency of occurrence of pore pressure in each interval, thereby obtaining the probability density distribution of the pore pressure in each interval;
performing pressure measurement sampling or drill pipe stratum testing on the ultra-temperature high-pressure exploratory well, and obtaining the pore pressure data sample according to a test result;
2) Acquiring a vertical well fracture pressure data sample, and equally dividing the vertical well fracture pressure data sample into a plurality of interval units from the lowest value to the highest value for statistics to obtain the occurrence frequency of the vertical well fracture pressure in each interval, thereby obtaining the probability density distribution of the vertical well fracture pressure in each interval;
floor drain experiments are carried out on the ultra-high temperature and high pressure exploratory well, and a vertical well fracture pressure data sample is obtained according to experimental results and a bottom hole pressure measuring value when a leak occurs in the drilling process;
3) Describing a probability density curve of pore pressure and a probability density curve of vertical well fracture pressure by utilizing a double-parameter Weibull function, respectively fitting to obtain shape parameters alpha and alpha 'and scale parameters beta and beta' by utilizing a least square method, and substituting the shape parameters alpha and alpha 'and the scale parameters beta and beta' into a function to obtain a probability density function expression of the pore pressure and a probability density function expression of the vertical well fracture pressure;
4) Integrating the probability density function of the pore pressure and the probability density function of the vertical well fracture pressure respectively to obtain a cumulative probability function expression of the pore pressure and a cumulative probability function expression of the vertical well fracture pressure;
5) Based on the cumulative probability of the vertical well fracture pressure, obtaining a cumulative probability function expression of the vertical well safety pressure according to a basic rule of reciprocal event probability operation;
6) Under the actual condition that the directional well is not generally subjected to fracture pressure test, according to the analytic solution of the fracture pressure proportion of the directional well and the vertical well, a cumulative probability function expression of the safety pressure of the directional well is obtained;
7) And according to a probability algorithm, carrying out probability multiplication on the cumulative probability of the pore pressure and the cumulative probability of the directional well safety pressure, and finally obtaining a safety drilling probability value of the ultrahigh-temperature high-pressure directional well, wherein the higher the value is, the lower the drilling risk is.
2. The evaluation method according to claim 1, characterized in that: in the step 3), the probability density function expression of the pore pressure is shown as a formula (1):
the probability density function expression of the vertical well fracture pressure is shown as the formula (2):
wherein f (P p ) Represents the probability density of pore pressure, f (P) f ) Represents the probability density, P, of the fracture pressure of the vertical well p Represents pore pressure, P f The method comprises the steps of representing the magnitude of the vertical well fracture pressure, alpha representing the shape parameter of the pore pressure dual-parameter Weibull function, beta representing the scale parameter of the pore pressure dual-parameter Weibull function, alpha 'representing the shape parameter of the vertical well fracture pressure dual-parameter Weibull function, and beta' representing the scale parameter of the vertical well fracture pressure dual-parameter Weibull function.
3. The evaluation method according to claim 2, characterized in that: in the step 4), the cumulative probability function expression of the pore pressure is shown as a formula (3):
the cumulative probability function expression of the vertical well fracture pressure is shown as the formula (4):
wherein P (P p ) Represents the cumulative probability of pore pressure, P (P f ) Representing the cumulative probability of fracture pressure for a vertical well.
4. A method of evaluating according to claim 3, wherein: in step 5), the cumulative probability function expression of the vertical well safety pressure is shown as the formula (5):
wherein,representing safe accumulation probability of fracture pressure of the vertical well; p (P) f ) Representing the probability of pressure build-up of a vertical well fracture.
5. The method of evaluating according to claim 4, wherein: in step 6), the cumulative probability function expression of the directional well safety pressure is shown as the formula (6):
wherein K represents the ratio of directional well to vertical well fracture pressure.
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| 《莺琼盆地高温高压钻井工程风险定量评价方法》;黄熠 等;《中国海上油气》;第31卷(第4期);119-124 * |
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