A Probability Quantification Method for Hybrid Multi-Criteria Collapse Pressure Based on GMM

Abstract

The present invention belongs to the technical field of deep formation drilling and completion, and discloses a method for quantitatively analyzing the probability of mixed multi-criterion collapse pressure based on GMM, which includes collecting samples of geomechanical parameters and performing standardization processing; conducting cluster analysis on the standardized data of the geomechanical parameter samples; constructing a parameter uncertainty quantification model in combination with the geomechanical parameter samples; constructing a wellbore stability evaluation model based on the wellbore stress distribution and different rock failure criteria, and setting the probability weight coefficients of different criterion models; randomly generating N groups of sampling data based on the parameter uncertainty quantification model and calculating the wellbore collapse pressure; and quantifying the probability result of the collapse pressure in combination with the Monte Carlo method. The present invention can use the geomechanical parameter samples to realize the quantification of the high-dimensional joint probability distribution of the parameters, and further combine multiple failure criteria to construct a multi-criterion collapse pressure probability model for the wellbore, thereby effectively improving the efficiency of the uncertainty quantification work of the wellbore collapse pressure.

Description

Technical Field

[0001] The present invention relates to a method for quantitatively calculating the probability of mixed multi-criterion collapse pressure based on GMM, belonging to the technical field of oil and gas drilling and completion engineering. Background Art

[0002] In drilling engineering, the minimum drilling fluid column pressure required to maintain wellbore stability is usually defined as the collapse pressure. When the drilling mud pressure is lower than this pressure, the wellbore rock often exhibits shear failure, which further leads to large-scale caving of the wellbore rock, seriously interfering with the safe implementation of the drilling engineering.

[0003] At the same time, the uncertainty characteristics of geotechnical engineering seriously interfere with the accurate analysis of underground engineering, and further lead to interference in the quantification of wellbore collapse pressure due to parameter uncertainty and model uncertainty; in particular, there are multiple rock failure criteria for wellbore stability evaluation and analysis, such as: Mohr-Coulomb criterion, Mogi-Coulomb criterion, Modified Lade criterion, and Modified Wiebols-Cook criterion, etc. Therefore, the uncertainty of geomechanical parameters and the ambiguity of rock failure criterion selection further exacerbate the uncertainty quantification process of wellbore collapse pressure.

[0004] Currently, there are various theoretical calculation methods for wellbore collapse pressure. For example, the invention patent with the authorization number CN114547906B authorized by Southwest Petroleum University authorizes a wellbore stability logging interpretation method for deep formations containing weak structural planes. This method overcomes the deficiencies of common wellbore stability logging interpretation methods, can more accurately predict the wellbore stability of deep formations containing weak structural planes, and thus effectively guide the safe and efficient drilling of deep complex formations.

[0005] The invention patent with the authorization number CN114635684B authorized by China National Petroleum Corporation and CNPC Chuanqing Drilling Engineering Company Limited authorizes a wellbore stability evaluation method, a calculation method and system for wellbore collapse pressure. This method directly establishes the relationship between the well logging diameter data of completion and the allowable hole enlargement rate and collapse pressure, facilitating the comparison analysis and application of actual drilling site data.

[0006] Although the above two patents and other existing technical solutions have achieved certain technical effects, they have not fully considered the influence of geomechanical parameter uncertainty and the ambiguity of rock failure criterion selection, resulting in serious obstruction in the uncertainty quantification of wellbore collapse pressure in complex formations, thus affecting the implementation of underground drilling engineering. Summary of the Invention

[0007] To overcome the defects existing in the prior art, the present invention aims to provide a method for quantifying the probability of collapse pressure of a hybrid multi-criterion based on GMM. The present invention can utilize geological mechanics parameter samples to quantify the high-dimensional joint probability distribution of parameters, and further combine multiple failure criteria to construct a multi-criterion collapse pressure probability model for the wellbore, thereby effectively improving the quantification of the uncertainty of the wellbore collapse pressure.

[0008] The technical solution provided by the present invention to solve the above technical problems is: a method for quantifying the probability of collapse pressure of a hybrid multi-criterion based on GMM, comprising the following steps:

[0009] Collect geological mechanics parameter samples according to well logging data and indoor experimental results, and perform standardization processing;

[0010] Combine the DBSCAN algorithm to perform clustering analysis on the standardized data of geological mechanics parameter samples to obtain the number of clusters;

[0011] Set the number of components of the GMM model to the number of clusters, and construct a parameter uncertainty quantification model in combination with geological mechanics parameter samples;

[0012] Based on the wellbore stress distribution, construct a wellbore stability evaluation model in combination with different rock failure criteria, and set the probability weight coefficients of different criterion models;

[0013] Randomly generate N groups of sampling data based on the parameter uncertainty quantification model, and calculate the wellbore collapse pressure according to the probability weight coefficients;

[0014] Statistically analyze the calculation results of the wellbore collapse pressure under N groups of sampling data, and combine the Monte Carlo method to quantify the probability results of the collapse pressure.

[0015] A further technical solution is that the geological mechanics parameters include horizontal in-situ stress, overburden rock pressure, pore pressure, Poisson's ratio, uniaxial compressive strength, cohesion, and internal friction angle.

[0016] A further technical solution is that the DBSCAN algorithm defines clusters by delineating a radius around the sample points, setting the minimum number of points minPts, and then calculating the number of data points within the radius.

[0017] A further technical solution is that the theoretical formula of the DBSCAN algorithm is:

[0018]

[0019]

[0020] In the formula: is the number of sub-sample sets; minPts is the minimum number of points; p , qis a sample point; is a sample point p , q is the Euclidean distance; is the radius.

[0021] A further technical solution is that the specific theoretical form of the GMM model is:

[0022]

[0023]

[0024] In the formula: is n the general form of a D-dimensional Gaussian distribution; is the mean vector of the k th Gaussian distribution; is the covariance matrix of the k th Gaussian distribution; is the input n dimensional vector; K is the number of components of the GMM model; is the k th weight coefficient of the Gaussian distribution; T is the transpose of the matrix .

[0025] A further technical solution is that the wellbore stress distribution includes:

[0026]

[0027] In the formula: , , , , , are respectively the radial effective stress, circumferential effective stress, axial effective stress of the rock around the well in the cylindrical coordinate system, plane shear stress, plane shear stress, and plane shear stress, MPa; , , , , , are respectively direction effective stress, direction effective stress, direction effective stress, plane shear stress, plane shear stress, and plane shear stress, MPa; is the drilling fluid column pressure, MPa; is the pore pressure, MPa; v is the Poisson's ratio, dimensionless; is the wellbore failure angle, °.

[0028] A further technical solution is that the different rock failure criteria include the Mohr-Coulomb criterion, the Modified Lade criterion, the Modified Wiebols-Cook criterion, and the Mogi-Coulomb criterion.

[0029] A further technical solution is that the wellbore stability evaluation model includes two parts: the wellbore stress distribution and the rock failure criterion, and the minimum drilling fluid density to maintain the wellbore is solved by substituting the wellbore stress distribution into the rock failure criterion as the wellbore collapse pressure.

[0030] A further technical solution is that the process of calculating the wellbore collapse pressure based on the probability weight coefficient is as follows:

[0031] Generate a random number in the interval [0, 1] r ; Use the random number r to compare one by one with the sum of the probability weight coefficients of different numbers of rock failure criteria until the random number r is greater than the sum of the probability weight coefficients, then output the number of rock failure criteria l , and correspondingly select the l th rock failure criterion to calculate the collapse pressure; repeat the above calculation process until N groups of sampling data are calculated.

[0032] A further technical solution is that the probability formula for quantifying the collapse pressure in combination with the Monte Carlo method is:

[0033]

[0034] In the formula: is the probability of the collapse pressure; is the number of collapse pressures equal to in the sample set; is the total number of samples; is the interval width.

[0035] The present invention also provides an electronic device, including:

[0036] One or more processors;

[0037] A storage device on which one or more programs are stored;

[0038] When the one or more programs are executed by the one or more processors, the one or more processors are caused to implement the GMM-based hybrid multi-criterion collapse pressure probability quantification method of the present invention as described above.

[0039] The present invention also provides a storage medium, on which a computer program is stored, wherein when the computer program is executed by a processor, the GMM-based hybrid multi-criterion collapse pressure probability quantification method of the present invention as described above is implemented.

[0040] The present invention has the following beneficial effects: The GMM-based hybrid multi-criterion collapse pressure probability quantification method provided by the present invention collects geomechanical parameter samples and combines them with the DBSCAN algorithm to predict the number of components of the mixture Gaussian probability model; further uses GMM to quantify the uncertainty of geomechanical parameters under the condition of correlated features and complex distributions; by determining the weight coefficients under different criteria, a multi-criterion wellbore collapse pressure probability model under the uncertainty of geomechanical parameters is constructed. The present invention considers the influence of the correlation and uncertainty of reservoir geomechanical parameters, and through the combination of GMM and DBSCAN, provides theoretical and technical guidance for the uncertainty analysis of wellbore collapse pressure. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is the sampling data of the geomechanical parameter samples obtained by combining GMM with the DBSCAN algorithm in the embodiment of the present invention (basic data source: Well X);

[0042] Figure 2 It is the wellbore multi-criterion collapse pressure probability result obtained in the embodiment of the present invention (basic data source: Well X). DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] The technical solutions of the present invention will be described clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the protection scope of the present invention.

[0044] A GMM-based hybrid multi-criterion collapse pressure probability quantification method of the present invention includes the following steps:

[0045] Step 1: Collect geomechanical parameter samples according to well logging data and indoor experimental results, and perform standardization processing to obtain standardized data of geomechanical parameter samples;

[0046] wherein the geomechanical parameters include horizontal in-situ stress, overburden rock pressure, pore pressure, Poisson's ratio, uniaxial compressive strength, cohesion, and internal friction angle;

[0047] The formula for the standardization process is as follows:

[0048]

[0049] In the formula: is the original sample of geomechanical parameters; is the mean value of the geomechanical parameter samples; is the standard deviation of the geomechanical parameter samples; is the standardized sample data;

[0050] Step 2: Combine the DBSCAN algorithm to perform clustering analysis on the standardized data of the geomechanical parameter samples to obtain the number of clusters;

[0051] Among them, the DBSCAN algorithm defines clusters by delimiting a radius around the sample points, setting the minimum number of points minPts, and then calculating the number of data points within the radius to define clusters.

[0052] The theoretical formula of the DBSCAN algorithm is as follows:

[0053]

[0054]

[0055] In the formula: is the number of sub-sample sets; minPts is the minimum number of points; p , q is the sample point; is the sample point p , q 's Euclidean distance; is the radius;

[0056] Step 3: Set the number of components of the GMM model to the number of clusters, and construct a parameter uncertainty quantification model in combination with the geomechanical parameter samples;

[0057] Among them, the specific theoretical form of the GMM model (Gaussian mixture model) is as follows:

[0058]

[0059]

[0060] In the formula: is the general form of the n -dimensional Gaussian distribution; is the mean vector of the k th Gaussian distribution; is the covariance matrix of the k th Gaussian distribution; is the inputn dimensional vector; K is the number of components of the GMM model; is the k weight coefficient of the T th Gaussian distribution; is the transpose of the matrix

[0061] where satisfies the following conditions:

[0062]

[0063]

[0064] Step 4: Construct a wellbore stability evaluation model based on the wellbore stress distribution and different rock failure criteria, and set the probability weight coefficients of different criterion models;

[0065] where the wellbore stress distribution includes:

[0066]

[0067] In the formula: , , , , , are the radial effective stress, circumferential effective stress, axial effective stress of the rock around the well in the cylindrical coordinate system, plane shear stress, plane shear stress, and plane shear stress, MPa; , , , , , are respectively direction effective stress, direction effective stress, direction effective stress, plane shear stress, plane shear stress, and plane shear stress, MPa; is the drilling fluid hydrostatic pressure, MPa; is the pore pressure, MPa; v is the Poisson's ratio, dimensionless; is the wellbore failure angle, °;

[0068] The in-situ stress field variables in the rectangular coordinate system at the wellbore are obtained through the following relational expressions:

[0069]

[0070] In the formula: is the maximum horizontal in-situ stress, MPa; is the minimum horizontal in-situ stress, MPa; is the overburden rock pressure, MPa; w is the angle between the maximum in-situ stress and the wellbore azimuth, °; is the well deviation angle;

[0071] The rock failure criteria include Mohr-Coulomb criterion, Modified Lade criterion, Modified Wiebols-Cook criterion, and Mogi-Coulomb criterion;

[0072] Among them, Mohr-Coulomb criterion:

[0073] Under the condition of ignoring the influence of the intermediate stress, the Mohr-Coulomb criterion believes that rock failure comes from the shear stress on the shear plane overcoming the sum of the inherent cohesive force of the rock and the frictional force on the shear plane, that is:

[0074]

[0075] In the formula: σ c Uniaxial compressive strength of rock, MPa; ψ is the internal friction angle, °.

[0076] Modified Lade criterion:

[0077]

[0078]

[0079]

[0080] In the formula: , , are the first, second, and third effective principal stresses, MPa; S , η are material constants, depending on the cohesive force and the internal friction angle; C o is the cohesive force of the rock, MPa;

[0081] Modified Wiebols-Cook criterion:

[0082]

[0083] Among them, the coefficients A , B and CIt can be obtained through the following relational expressions:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] In the formula: is the first invariant of the principal stress, MPa; is the second invariant of the stress deviator, MPa; is the first invariant of the stress deviator, MPa; is the coefficient related to the rock strength, MPa; q is the material coefficient related to the cohesion;

[0090] Mogi-Coulomb criterion:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] In the formula: is the octahedral shear stress, MPa; is the mean normal stress, MPa; a , b are the coefficients related to the material.

[0097] Probability weight coefficient represents the selection probability of the rock failure criterion. The larger its value, the higher the possibility of applying this criterion. Among them m represents the total number of rock failure criteria and satisfies that the sum of all weight coefficients is 1;

[0098] The wellbore stability evaluation model solves for the minimum drilling fluid density to maintain the wellbore as the wellbore collapse pressure by substituting the wellbore stress distribution into the rock failure criterion;

[0099] Step Five: Randomly generate N groups of sampling data based on the parameter uncertainty quantification model, and calculate the wellbore collapse pressure according to the probability weight coefficient;

[0100] Among them, the process of calculating the wellbore collapse pressure according to the probability weight coefficient includes: generating a random number in the interval [0, 1] r ; using the random number r to compare one by one with the sum of the probability weight coefficients of different numbers of rock failure criteria until the random number r is greater than the sum of the probability weight coefficients , then output the number of rock failure criteria l , and correspondingly select the l th rock failure criterion to calculate the collapse pressure; repeat the above calculation process until N groups of sampling data are calculated.

[0101] Step 6. Statistically analyze the calculation results of the wellbore collapse pressure under N groups of sampling data, and combine the Monte Carlo method to quantify the probability results of the collapse pressure;

[0102] The probability formula for quantifying the collapse pressure by combining the Monte Carlo method is as follows:

[0103]

[0104] In the formula: is the probability of the collapse pressure; is the number of times the collapse pressure in the sample set is equal to ; is the total number of samples; is the interval width.

[0105] Embodiment

[0106] In this embodiment, the relevant parameter sources of the hybrid multi-criterion collapse pressure probability quantification method based on GMM for Well X are shown in Table 1 (the geomechanical parameter samples also come from Well X, see Figure 1 shown):

[0107] Table 1 Geomechanical Parameter Data Table

[0108]

[0109] In this embodiment, the number of components obtained is K = 7.

[0110] According to the above parameters, the sampling data of the geomechanical parameter samples obtained by combining GMM with the DBSCAN algorithm as shown in Figure 1 can be obtained (the scatter points in Figure 1 respectively represent the geomechanical parameter samples and the sampling data), and Figure 2 the probability results of the wellbore multi-criterion collapse pressure obtained in the embodiment of the present invention as shown in Figure 2The left curve in the figure is the probability density distribution of the collapse pressure, and the shaded area corresponds to the high-probability distribution area of the collapse pressure; the right curve is the reliability distribution curve of the collapse pressure).

[0111] The embodiment of the present invention also provides a GMM-based hybrid multi-criterion collapse pressure probability quantification system for implementing the GMM-based hybrid multi-criterion collapse pressure probability quantification method as described above in the present invention, including:

[0112] A geomechanical parameter sample sampling module combining GMM and DBSCAN algorithm: used to analyze the uncertainty characteristics of the current geomechanical samples and construct a high-dimensional joint probability distribution function that meets the above uncertainty characteristics; thereby further realizing data sampling that conforms to the uncertainty of the geomechanical parameter samples;

[0113] A hybrid multi-criterion collapse pressure probability quantification module: used to construct a wellbore stability evaluation model based on the wellbore stress distribution and different rock failure criteria, and calculate the probability model of the wellbore collapse pressure by inputting the probability weight coefficient.

[0114] The embodiment of the present invention also provides a corresponding electronic device and a computer-readable storage medium for implementing the solution provided by the embodiment of the present invention.

[0115] Wherein, the electronic device includes a storage device and a processor, the storage device is used to store instructions or codes, and the processor is used to execute the instructions or codes so that the electronic device executes the GMM-based hybrid multi-criterion collapse pressure probability quantification method described in any embodiment of the present application.

[0116] In practical applications, the computer-readable storage medium can adopt any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium.

[0117] As mentioned above, it is not a limitation to the present invention in any form. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications within the scope of the technical solution of the present invention to make equivalent embodiments with equivalent changes. However, as long as it does not depart from the content of the technical solution of the present invention, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention all fall within the scope of the technical solution of the present invention.

Claims

1. A hybrid multi-criteria collapse pressure probability quantification method based on GMM, characterized in that: The following steps are involved: Collect geomechanical parameter samples based on well logging data and laboratory experimental results, and perform standardized processing; Cluster analysis of geomechanical parameter sample standardization data was performed using the DBSCAN algorithm to obtain the number of clusters; The number of components of the GMM model is set as the number of clusters, and a parameter uncertainty quantification model is constructed in combination with geomechanical parameter samples; A wellbore stability evaluation model is constructed based on the wellbore stress distribution and different rock failure criteria, and the probability weight coefficients of different criterion models are set; Based on the parameter uncertainty quantification model, N groups of sampling data are randomly generated, and the wellbore collapse pressure is calculated according to the probability weight coefficient; The process of calculating the wellbore collapse pressure based on the probability weight coefficient is as follows: Generate a random number in the interval [0,1] r ; Using random numbers r Compare the probability weight coefficients of different numbers of rock failure criteria one by one until the random number r If it is greater than the sum of the probability weight coefficients, the number of rock failure criteria is output l , select the l The collapse pressure is calculated by using a rock failure criterion; the above calculation process is repeated until N groups of sampling data are calculated; The calculation results of wellbore collapse pressure under N groups of sampling data are statistically analyzed, and the probability results of collapse pressure are quantified by combining Monte Carlo method.

2. The hybrid multi-criteria collapse pressure probability quantification method based on GMM according to claim 1 is characterized in that: The geomechanical parameters include horizontal ground stress, overburden rock pressure, pore pressure, Poisson's ratio, uniaxial compressive strength, cohesion and internal friction angle.

3. The hybrid multi-criteria collapse pressure probability quantification method based on GMM according to claim 1, characterized in that: The DBSCAN algorithm defines a cluster by defining a radius around a sample point, setting a minimum number of points minPts, and then calculating the number of data points within the radius.

4. The hybrid multi-criteria collapse pressure probability quantification method based on GMM according to claim 3 is characterized in that: The theoretical formula of the DBSCAN algorithm is: Where: is the number of sub-sample sets; minPts is the minimum number of points; p , q is the sample point; For sample points p , q The Euclidean distance of is the radius.

5. The hybrid multi-criteria collapse pressure probability quantification method based on GMM according to claim 1, characterized in that: The specific theoretical form of the GMM model is: Where: for n The general form of the Gaussian distribution; For the k The mean vector of the Gaussian distribution; For the k The covariance matrix of the Gaussian distribution; For input n dimensional vector; K is the number of components of the GMM model; For the k The weight coefficient of the Gaussian distribution; T For the matrix The transpose of .

6. The hybrid multi-criteria collapse pressure probability quantification method based on GMM according to claim 1, characterized in that: The wellbore stress distribution includes: Where: , , , , , They are the radial effective stress, circumferential effective stress, axial effective stress, Plane shear stress, Plane shear stress and Plane shear stress, MPa; , , , , , They are Directional effective stress, Directional effective stress, Directional effective stress, Plane shear stress, Plane shear stress and Plane shear stress, MPa; is the drilling fluid column pressure, MPa; is the pore pressure, MPa; v is Poisson’s ratio, dimensionless; is the well circumference failure angle, °.

7. The hybrid multi-criteria collapse pressure probability quantification method based on GMM according to claim 1, characterized in that: The different rock failure criteria include the Mohr-Coulomb criterion, the Modified Lade criterion, the Modified Wiebols-Cook criterion and the Mogi-Coulomb criterion.

8. The hybrid multi-criteria collapse pressure probability quantification method based on GMM according to claim 1, characterized in that: The wellbore stability evaluation model includes two parts: wellbore stress distribution and rock failure criterion, and the wellbore stress distribution is substituted into the rock failure criterion to solve the minimum drilling fluid density to maintain the wellbore as the wellbore collapse pressure.

9. The hybrid multi-criteria collapse pressure probability quantification method based on GMM according to claim 1, characterized in that: The probability formula for quantifying collapse pressure by combining the Monte Carlo method is: Where: is the probability of collapse pressure; The collapse pressure of the sample set is equal to the number of is the total number of samples; is the interval width.

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