CN112347424A - Method for evaluating safe drilling probability of ultra-high temperature and high pressure development based on Weibull function - Google Patents
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Abstract
The invention discloses an evaluation method of ultrahigh temperature and high pressure development safe drilling probability based on Weibull function. The method comprises the following steps: collecting pore pressure data samples and vertical well fracture pressure data samples of the ultrahigh-temperature high-pressure stratum; obtaining probability density distribution of the interval pore pressure and the vertical well fracture pressure according to the occurrence frequency of the interval pore pressure and the vertical well fracture pressure; 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 accumulative probability expression of the vertical well safety pressure; determining a cumulative probability expression of the safety pressure of the directional well; and calculating the safe drilling probability value of the ultrahigh temperature and high pressure directional well. By utilizing the method, the safe drilling probability can be evaluated before the development well is drilled, high-risk operation is avoided, the cost and safety accidents are reduced, and the method has important significance for the development of ultra-high temperature and high pressure oil and gas fields.
Description
Technical Field
The invention relates to an evaluation method of ultrahigh temperature and high pressure development safe drilling probability based on Weibull function, belonging to the field of oil drilling and production.
Background
The deep stratum temperature of the ultrahigh-temperature high-pressure oil and gas field exceeds 180 ℃, the pore pressure coefficient exceeds 2.20, the vertical well fracture pressure coefficient 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 economic development of the ultrahigh-temperature and high-pressure oil-gas field, the safe drilling probability value of a development well (a directional well) is quantitatively evaluated in the pre-drilling stage based on the statistical analysis of drilled wells.
Compared with normal temperature and pressure and common high temperature and pressure areas, the formation temperature and pressure in the ultrahigh temperature and 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 high-pressure region: the formation temperature is between 150 ℃ and 180 ℃, and the pore pressure coefficient is between 1.8 and 2.2; 3) ultrahigh temperature and high pressure region: the formation temperature exceeds 180 ℃ and the pore pressure coefficient exceeds 2.2. In the aspect of safe drilling probability assessment, the uncertainty of the pore pressure and fracture pressure in the existing method is treated according to the 'assumption of normal distribution', which is a qualitative assumption and does not adopt measured value samples and probability statistical analysis. There is therefore a need for improvements over existing methods.
Disclosure of Invention
The invention aims to provide an evaluation method of the ultrahigh-temperature and high-pressure development safety drilling probability based on a Weibull function, which can accurately and quantitatively evaluate the safety probability of the ultrahigh-temperature and high-pressure oil and gas field development drilling.
The research object focuses on the ultrahigh-temperature high-pressure area, breaks through the limitations of normal-temperature normal-pressure and common high-temperature high-pressure areas, overcomes the hypothetical defects of the existing evaluation method, and realizes the quantitative evaluation of the safe drilling probability of the simulated drilling ultrahigh-temperature high-pressure development well from the angles of the measured value and the probability statistics of the drilled well under the ultrahigh temperature and the high pressure.
The invention provides an evaluation method of ultrahigh temperature and high pressure development safe drilling probability based on Weibull function, which comprises the following steps:
1) acquiring a pore pressure data sample of the ultrahigh-temperature and high-pressure stratum, and dividing the sample into a plurality of interval units at equal intervals from the lowest value to the highest value for statistics to obtain the frequency of pore pressure in each interval, and further obtain the probability density distribution of the pore pressure in each interval;
2) acquiring a vertical well fracture pressure data sample, and dividing the vertical well fracture pressure data sample into a plurality of interval units at equal intervals from a lowest value to a highest value for statistics to obtain the frequency of the vertical well fracture pressure in each interval, and further obtain the probability density distribution of the vertical well fracture pressure in each interval;
3) the probability density curve of the pore pressure and the probability density curve of the vertical well fracture pressure are described by using a double-parameter Weibull function, shape parameters alpha and alpha 'and scale parameters beta and beta' are respectively obtained by using a least square method through fitting, and the shape parameters alpha and alpha 'and the scale parameters beta and beta' are substituted 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) respectively integrating the probability density function of the pore pressure and the probability density function of the vertical well fracture pressure to obtain an accumulated probability function expression of the pore pressure and an accumulated 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 the basic rule of reciprocal event probability operation, wherein the cumulative probability of the vertical well safety pressure represents the cumulative probability that the vertical well is not fractured;
6) under the actual condition that the directional well is not subjected to fracture pressure test generally, obtaining an accumulative probability function expression of the directional well safety pressure according to an analytic solution of the ratio of the directional well to the vertical well fracture pressure, wherein the accumulative probability of the directional well safety pressure represents the accumulative probability that the directional well is not fractured;
7) and according to a probability operation basic rule, carrying out probability multiplication on the accumulated probability of the pore pressure and the accumulated probability of the directional well safety pressure to finally obtain the safe 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 evaluation method, in step 1), pressure measurement sampling (MDT) or drill pipe formation testing (DST) is performed on the ultrahigh-temperature and high-pressure exploration well, and the pore pressure data sample is obtained from a test result.
In the evaluation method, in the step 2), a floor drain experiment is carried out on the ultrahigh-temperature high-pressure exploration well, and the vertical well fracture pressure data sample is obtained according to the experiment result and the bottom hole pressure measurement value when leakage occurs in the drilling process.
In the evaluation method, in the step 3), regression fitting is respectively carried out on the two-parameter Weibull function of the pore pressure and the probability density of the vertical well fracture pressure by a least square method, so as to respectively obtain shape parameters alpha and alpha 'and scale parameters beta and beta', and obtain a two-parameter Weibull function expression representing the probability density of the pore pressure and the vertical well fracture pressure;
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 pore pressure probability density, f (P)f) Representing the probability density of vertical well fracture pressure, PpDenotes the pore pressure, PfThe method comprises the steps of expressing the size of the vertical well fracture pressure, expressing alpha, expressing the shape parameter of a pore pressure two-parameter Weibull function, expressing beta, expressing the scale parameter of the pore pressure two-parameter Weibull function, expressing alpha 'expressing the shape parameter of the vertical well fracture pressure two-parameter Weibull function, and expressing beta' expressing the scale parameter of the vertical well fracture pressure two-parameter Weibull function.
In the above evaluation method, in step 4), the cumulative probability function expression of the pore pressure is represented by formula (3):
the expression of the cumulative probability function 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 a vertical well fracture pressure.
In the above evaluation method, in step 5), the expression of the cumulative probability function of the vertical well safety pressure is as shown in formula (5):
wherein,
representing the cumulative probability of vertical well fracture pressure (safe); p (P)f) Indicating the probability of vertical well fracture pressure buildup.
In the above evaluation method, in step 6), the expression of the cumulative probability function of the safety pressure of the directional well is shown as formula (6):
wherein K represents the ratio of the directional well to the vertical well fracture pressure.
In the above-described evaluation method, in step 7), the cumulative probability P (P) of the pore pressure is calculated based on the probability algorithm basic rulep) And cumulative probability of directional well fracture pressure (safety)
And (4) multiplying the two to finally obtain the safe drilling probability value P (safe) of the ultrahigh-temperature and high-pressure directional well, wherein the higher the value is, the lower the drilling risk is.
According to the method, the safe drilling probability of the ultrahigh-temperature and high-pressure development well is obtained by utilizing measured value samples of the pore pressure and the fracture pressure of the ultrahigh-temperature and high-pressure exploration well based on a two-parameter Weibull probability density function and a 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 developed well by utilizing measured data samples of ultrahigh temperature and high pressure drilled well hole gap pressure and fracture pressure. The method can evaluate the drilling safety probability before the development of well drilling, avoid high-risk operation, reduce cost and safety accidents, and has important significance for the development of ultra-high temperature and high pressure oil and gas fields.
The method provided by the invention has clear and feasible technical route and wide data source, and can realize the probability evaluation of the safe drilling for the ultrahigh-temperature and high-pressure development.
Drawings
FIG. 1 is a flow chart of the evaluation method of the present invention.
FIG. 2 is a probability chart of safe drilling of the ultrahigh temperature and high pressure directional well obtained by the method.
FIG. 3 is a probability distribution diagram of formation pore pressure and circulating equivalent drilling fluid density at 1800m of a vertical well.
FIG. 4 is a probability distribution diagram of formation fracture pressure and circulating equivalent drilling fluid density at 1800m of a vertical well.
Detailed Description
The experimental procedures used in the following examples are all conventional procedures unless otherwise specified.
Materials, reagents and the like used in the following examples are commercially available unless otherwise specified.
The flow chart of the method for evaluating the probability of developing safe drilling at ultrahigh temperature and high pressure based on the Weibull function is shown in FIG. 1, and comprises the following steps:
1) acquiring a pore pressure data sample of the ultrahigh-temperature and high-pressure stratum according to a pressure measurement sampling (MDT) result and a drill pipe stratum testing (DST) result of the ultrahigh-temperature and high-pressure exploration well;
2) acquiring a vertical well fracture pressure data sample of an ultrahigh-temperature and high-pressure stratum according to floor drain experiment data of the ultrahigh-temperature and high-pressure exploration well and a bottom hole pressure measurement value when leakage occurs in the drilling process;
3) dividing the pore pressure and vertical well fracture pressure data samples obtained in the steps 1) and 2) into a plurality of interval units at equal intervals from the lowest value to the highest value for statistics, and respectively obtaining the 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 the samples respectively, and calculating to obtain probability density distribution of pore pressure and vertical well fracture pressure in each interval;
5) selecting a two-parameter Weibull function to respectively depict the probability densities of the pore pressure and the vertical well fracture pressure, wherein the expression is as follows, respectively fitting by using a least square method to obtain shape parameters alpha and alpha 'and scale parameters beta and beta' in the function, and substituting the shape parameters alpha and alpha 'and the scale parameters beta and beta' into the function to obtain the probability densities f (P) of the pore pressure and the vertical well fracture pressurep)、f(Pf) A function expression;
in the formula, f (P)p) Is the pore pressure probability density, f (P)f) Is the probability density of vertical well fracture pressure, PpIs pore pressure, PfThe method comprises the steps of obtaining a vertical well fracture pressure, wherein alpha is a shape parameter of a pore pressure two-parameter Weibull function, beta is a scale parameter of the pore pressure two-parameter Weibull function, alpha 'is a shape parameter of the vertical well fracture pressure two-parameter Weibull function, and beta' is a scale parameter of the vertical well fracture pressure two-parameter Weibull function;
6) at [0, + ∞]Integrating the probability density function of the pore pressure and the vertical well fracture pressure within the range to obtain the cumulative probability P (P) of the pore pressure and the vertical well fracture pressurep)、P(Pf) The function is expressed as follows:
in the formula, P (P)p) For the pore pressure buildup probability, P (P)f) Is the vertical well fracture pressure buildup probability.
7) Cumulative probability P (P) based on vertical well fracture pressuref) According to the basic rule of reciprocal event probability operation, the cumulative probability of the vertical well fracture pressure (safety) is obtained
The function expression:
in the formula,
representing the probability of the safe pressure accumulation of the vertical well; p (P)f) Indicating the probability of vertical well fracture pressure buildup.
8) Under the actual condition that the directional well is not subjected to the fracture pressure test generally, the cumulative probability function expression of the safety pressure of the directional well is obtained by analyzing the fracture pressure proportion K of the directional well and the vertical well
Wherein the analytic solution expression of K is as follows:
in the formula, Pf1＝3σH-(σh cos2ψ+σV sin2ψ)-Biot·Pp+St
Pf2＝3σh-(σH cos2ψ+σV sin2ψ)-Biot·Pp+St
In the formula, σHTo level maximum ground stress, σhFor horizontal minimum ground stress, Biot is the effective stress coefficient, θ is the azimuth angle, ψ is the well angle, P is the inclination anglepIs pore pressure, StIs the formation tensile strength.
9) Respectively obtaining the pore pressure cumulative probability P (P) by utilizing the step 6) and the step 8)p) And cumulative probability of directional well safety pressure
And then, performing probability multiplication on the two events according to a probability operation basic rule to finally obtain a safe drilling probability value P (safe) of the ultrahigh-temperature and high-pressure directional well, wherein the higher the value is, the lower the drilling risk is.
FIG. 2 is a diagram of the safe drilling probability of the ultrahigh-temperature high-pressure directional well, and it can be seen from the diagram that the method can quantitatively evaluate the safe drilling probability values of different well deviation development wells, and the larger the well deviation angle is, the lower the safe drilling probability value is; under the condition of a fixed well deviation angle, the drilling fluid density peak with higher safety probability is positioned on the right side.
In the conventional method (such as Shengya Nan, etc., a drilling engineering risk quantitative evaluation method [ J ] based on uncertainty analysis, China university of Petroleum institute: Nature science edition, 2019,43(02):91-96.) qualitatively judges through probability density distributions of pore pressure and fracture pressure respectively, for example, fig. 3 is a probability distribution graph of formation pore pressure and circulating equivalent drilling fluid density at 1800m of a certain vertical well, and fig. 4 is a probability distribution graph of formation fracture pressure and circulating equivalent drilling fluid density at 1800m of the certain vertical well. The "risk" is represented by the "intersection" of the histogram representing the formation pore pressure (left side in fig. 3, right side in fig. 4) with the histogram representing the fracture pressure (right side in fig. 3, left side in fig. 4), and the results are not truly quantified. It can be seen that the subjective factor-circulating equivalent drilling fluid density is included in the existing methods and is not 100% reflective of the objective characteristics of the formation. The existing method separates two risks of pore pressure and fracture pressure and carries out qualitative judgment respectively, but actually the safe drilling probability is determined by the two risks together. In the existing method, by assumption, the random variable of the pore pressure is considered to meet normal distribution, and actual measurement shows that the pore pressure and the fracture pressure in the ultrahigh-temperature and 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 an ultrahigh-temperature high-pressure exploitation well.
The invention eliminates the interference of subjective factors and truly reflects the objective characteristics of the stratum. By adopting a probability product method, the pore pressure and the fracture pressure are integrated, the safety probability value of the ultrahigh-temperature high-pressure directional well can be quantitatively obtained, and the method is suitable for directional development wells.
The above description is only an exemplary embodiment of the present invention, and should not be taken as limiting the scope of the invention, and any person skilled in the art should understand that they can make equivalent changes and modifications without departing from the concept and principle of the present invention. It should be noted that the components of the present invention are not limited to the above-mentioned whole application, and various technical features described in the present specification can be selected to be used alone or in combination according to actual needs, so that the present invention naturally covers other combinations and specific applications related to the present invention.
Claims (7)
1. A method for evaluating the probability of safe drilling for ultrahigh temperature and high pressure development based on Weibull function comprises the following steps:
1) acquiring a pore pressure data sample of the ultrahigh-temperature and high-pressure stratum, and dividing the sample into a plurality of interval units at equal intervals from the lowest value to the highest value for statistics to obtain the frequency of pore pressure in each interval, and further obtain the probability density distribution of the pore pressure in each interval;
2) acquiring a vertical well fracture pressure data sample, and dividing the vertical well fracture pressure data sample into a plurality of interval units at equal intervals from a lowest value to a highest value for statistics to obtain the frequency of the vertical well fracture pressure in each interval, and further obtain the probability density distribution of the vertical well fracture pressure in each interval;
3) the probability density curve of the pore pressure and the probability density curve of the vertical well fracture pressure are described by using a double-parameter Weibull function, shape parameters alpha and alpha 'and scale parameters beta and beta' are respectively obtained by using a least square method through fitting, and the shape parameters alpha and alpha 'and the scale parameters beta and beta' are substituted 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) respectively integrating the probability density function of the pore pressure and the probability density function of the vertical well fracture pressure to obtain an accumulated probability function expression of the pore pressure and an accumulated 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 the basic rule of reciprocal event probability operation;
6) under the actual condition that the directional well is not subjected to fracture pressure test generally, obtaining an accumulative probability function expression of the safety pressure of the directional well according to an analytic solution of the fracture pressure ratio of the directional well and the vertical well;
7) and according to a probability operation basic rule, carrying out probability multiplication on the accumulated probability of the pore pressure and the accumulated probability of the directional well safety pressure to finally obtain the safe 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, wherein: in the step 1), pressure measurement sampling or drill pipe stratum testing is carried out on the ultrahigh-temperature high-pressure exploratory well, and the pore pressure data sample is obtained according to the testing result.
3. The evaluation method according to claim 1 or 2, characterized in that: and 2) performing a floor drain experiment on the ultrahigh-temperature high-pressure exploration well, and obtaining the vertical well fracture pressure data sample according to an experiment result and a bottom hole pressure measurement value when leakage occurs in the drilling process.
4. The evaluation method according to any one of claims 1 to 3, wherein: in the step 3), the expression of the probability density function 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 pore pressure probability density, f (P)f) Representing the probability density of vertical well fracture pressure, PpDenotes the pore pressure, PfThe method is characterized by representing the size of the vertical well fracture pressure, alpha represents the shape parameter of a pore pressure two-parameter Weibull function, beta represents the scale parameter of the pore pressure two-parameter Weibull function, and alpha' represents the vertical well fracture pressure two-parameter Weibull functionThe shape parameter of the number, β', represents the scale parameter of the straight well fracture pressure two-parameter Weibull function.
5. The evaluation method according to any one of claims 1 to 4, wherein: in the step 4), the expression of the cumulative probability function of the pore pressure is shown as the formula (3):
the expression of the cumulative probability function 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 a vertical well fracture pressure.
6. The evaluation method according to any one of claims 1 to 5, wherein: in the step 5), the expression of the cumulative probability function of the vertical well safety pressure is shown as the formula (5):
wherein,
representing the cumulative probability of vertical well fracture pressure (safe); p (P)f) Indicating the probability of vertical well fracture pressure buildup.
7. The evaluation method according to any one of claims 1 to 6, wherein: in the step 6), the expression of the cumulative probability function of the safety pressure of the directional well is shown as the formula (6):
wherein K represents the ratio of the directional well to the vertical well fracture pressure.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113177337A (en) * | 2021-04-20 | 2021-07-27 | 扬州大学 | Reed harvester safety evaluation method based on correlation factor characteristic value fluctuation interval |
| CN113177337B (en) * | 2021-04-20 | 2023-05-26 | 扬州大学 | Reed harvester safety assessment method based on association factor characteristic value fluctuation interval |
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