GMM-based mixed multi-criterion collapse pressure probability quantification method

Abstract

The invention belongs to the technical field of deep stratum drilling and completion, and discloses a GMM-based mixed multi-criterion collapse pressure probability quantification method, which comprises the following steps: collecting geomechanical parameter samples, and carrying out standardization processing; carrying out clustering analysis on the geomechanical parameter sample standardized data; constructing a parameter uncertainty quantitative model in combination with a geomechanical parameter sample; constructing a borehole wall stability evaluation model according to borehole wall stress distribution in combination with different rock failure criteria, and setting probability weight coefficients of different criterion models; randomly generating N groups of sampling data based on the parameter uncertainty quantitative model, and calculating borehole wall collapse pressure; and a probability result of collapse pressure is quantified in combination with a Monte Carlo method. According to the method, quantification of parameter high-dimensional joint probability distribution can be realized by using geomechanical parameter samples, and a well wall multi-criterion collapse pressure probability model can be constructed by further combining multiple failure criteria, so that the efficiency of well wall collapse pressure uncertainty quantification work is effectively improved.

Description

Technical Field

[0001] The invention relates to a hybrid multi-criteria collapse pressure probability quantification method based on GMM, belonging to the technical field of oil and gas drilling and completion. Background Art

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

[0003] At the same time, the uncertainty characteristics of geological engineering seriously interfere with the precise analysis of underground engineering, and further lead to the interference of parameter uncertainty and model uncertainty on the quantification of wellbore collapse pressure; in particular, there are a variety of 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 aggravate the uncertainty quantification process of wellbore collapse pressure.

[0004] At present, there are many methods for theoretical calculation of wellbore collapse pressure. For example, the invention patent of Southwest Petroleum University with authorization number CN114547906B authorizes a wellbore stability logging interpretation method for deep formations with weak structural surfaces. This method overcomes the shortcomings of the commonly used wellbore stability logging interpretation methods and can more accurately predict the wellbore stability of deep formations with weak structural surfaces, thereby effectively guiding safe and efficient drilling in deep complex formations.

[0005] The invention patent with authorization number CN114635684B of China National Petroleum Corporation and China National Petroleum Corporation Sichuan Qing Drilling Engineering Co., Ltd. authorized the wellbore stability evaluation method and the wellbore collapse pressure calculation method and system. This method directly establishes the relationship between the completion electrical logging wellbore data and the allowable expansion rate and collapse pressure, which is convenient for the comparative 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 failed to fully consider the influence of uncertainty in geomechanical parameters and ambiguity in the selection of rock failure criteria, resulting in serious obstruction in the quantification of uncertainty in wellbore collapse pressure in complex formations, thus affecting the implementation of underground drilling projects. Summary of the invention

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

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

[0009] A further technical solution is that the geomechanical parameters include horizontal ground stress, overlying rock pressure, pore pressure, Poisson's ratio, uniaxial compressive strength, cohesion and internal friction angle.

[0010] A further technical solution is 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.

[0011] A further technical solution is that the theoretical formula of the DBSCAN algorithm is:

[0012]

[0013] Where: is the number of subsample 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.

[0014] A further technical solution is that the specific theoretical form of the GMM model is:

[0015]

[0016] 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 .

[0017] A further technical solution is that the well wall stress distribution includes:

[0018] 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, °.

[0019] 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.

[0020] A further technical solution is 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.

[0021] A further technical solution is that the process of calculating the wellbore collapse pressure based on the probability weight coefficient is: 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 based on the rock failure criterion; the above calculation process is repeated until N groups of sampling data are calculated.

[0022] A further technical solution is that the probability formula for quantifying the collapse pressure by combining the Monte Carlo method is:

[0023] 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.

[0024] The present invention also provides an electronic device, comprising: one or more processors; a storage device having one or more programs stored thereon; When the one or more programs are executed by the one or more processors, the one or more processors implement the GMM-based hybrid multi-criteria collapse pressure probability quantification method of the present invention as described above.

[0025] The present invention also provides a storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the hybrid multi-criteria collapse pressure probability quantification method based on GMM as described above is implemented in the present invention.

[0026] The present invention has the following beneficial effects: the hybrid multi-criteria collapse pressure probability quantification method based on GMM provided by the present invention collects geomechanical parameter samples and combines with DBSCAN algorithm to predict the number of components of the mixed Gaussian probability model; GMM is further used to realize the uncertainty quantification of geomechanical parameters with correlation characteristics and complicated distribution; by determining the weight coefficients under different criteria, the multi-criteria wellbore collapse pressure probability model under the uncertainty of geomechanical parameters is constructed. The present invention takes into account the correlation and uncertainty effects of reservoir geomechanical parameters, and provides theoretical and technical guidance for the uncertainty analysis of wellbore collapse pressure through the combination of GMM and DBSCAN. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The sampling data of geomechanical parameter samples obtained by using GMM combined with DBSCAN algorithm in the embodiment of the present invention (basic data source: X well); Figure 2 Result of multi-criteria wellbore collapse pressure probability obtained in the embodiment of the present invention (basic data source: Well X). DETAILED DESCRIPTION

[0028] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] A hybrid multi-criteria collapse pressure probability quantification method based on GMM of the present invention comprises the following steps: Step 1: Collect geomechanical parameter samples based on well logging data and indoor experimental results, and perform standardization processing to obtain geomechanical parameter sample standardized data; The geomechanical parameters include horizontal ground stress, overburden rock pressure, pore pressure, Poisson's ratio, uniaxial compressive strength, cohesion and internal friction angle; The formula for the standardization process is:

[0030] Where: is the original geomechanical parameter sample; is the sample mean of geomechanical parameters; is the sample standard deviation of geomechanical parameters; is the standardized sample data; Step 2: Cluster analysis is performed on the standardized data of geomechanical parameter samples using the DBSCAN algorithm to obtain the number of clusters; The DBSCAN algorithm is to define a radius around the sample point , and set the minimum number of points minPts, and then calculate the radius The number of data points within a cluster is used to define the cluster.

[0031] The theoretical formula of the DBSCAN algorithm is:

[0032]

[0033] Where: is the number of subsample 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; Step 3: Set the number of components of the GMM model as the number of clusters, and build a parameter uncertainty quantification model in combination with geomechanical parameter samples; The specific theoretical form of the GMM model (Gaussian mixture model) is:

[0034]

[0035] 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 in The following conditions are met:

[0036]

[0037] Step 4: Construct a wellbore stability evaluation model based on wellbore stress distribution and different rock failure criteria, and set probability weight coefficients of different criterion models; The stress distribution of the wellbore includes:

[0038] 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, °; The in-situ stress field variables in the rectangular coordinate system at the wellbore are obtained by the following relationship:

[0039] Where: is the maximum horizontal ground stress, MPa; is the minimum horizontal ground stress, MPa; is the overlying rock pressure, MPa; w is the angle between the maximum geostress and the wellbore azimuth, °; is the well inclination angle; The rock failure criteria include the Mohr-Coulomb criterion, the Modified Lade criterion, the Modified Wiebols-Cook criterion and the Mogi-Coulomb criterion; The Mohr-Coulomb criterion is: The Mohr-Coulomb criterion, ignoring the influence of intermediate stress, believes that rock failure comes from the shear stress on the shear surface overcoming the sum of the inherent cohesion of the rock and the friction on the shear surface, that is:

[0040] Where: σ c Uniaxial compressive strength of rock, MPa; ψ is the internal friction angle, °.

[0041] Modified Lade Guidelines:

[0042]

[0043]

[0044] Where: , , are the first, second and third effective principal stresses, MPa; S , η is a material constant, which depends on the cohesion and the internal friction angle; C o is the rock cohesion, MPa; Modified Wiebols-Cook Criteria:

[0045] Among them, the coefficient A , B and C It can be obtained through the following relationship:

[0046]

[0047]

[0048]

[0049]

[0050] Where: is the first invariant of the principal stress, MPa; is the second invariant of stress deviator, MPa; is the first invariant of stress deviator, MPa; is the correlation coefficient with rock strength, MPa; q is the material coefficient related to cohesion;

[0051]

[0052]

[0053]

[0054]

[0055] Where: is the octahedral shear stress, MPa; is the average normal stress, MPa; a , b is a coefficient related to the material.

[0056] Probability weight coefficient Represents the selection probability of rock failure criterion. The larger its value, the higher the possibility of applying the criterion. m Represents the total number of rock failure criteria, and the sum of all weight coefficients is 1; The wellbore stability evaluation model substitutes the wellbore stress distribution into the rock failure criterion to solve the minimum drilling fluid density to maintain the wellbore as the wellbore collapse pressure; Step 5: 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; The process of calculating the wellbore collapse pressure based on the probability weight coefficient includes: generating a random number in the interval [0,1] r ; Using random numbers r The sum of probability weight coefficients of rock failure criteria one by one and with different numbers Compare until the random number r Greater than the sum of the probability weight coefficients , then the number of rock failure criteria is output l , select the l The collapse pressure is calculated based on the rock failure criterion; the above calculation process is repeated until N groups of sampling data are calculated.

[0057] Step 6: Calculate the wellbore collapse pressure calculation results under N groups of sampling data, and quantify the probability results of collapse pressure by using Monte Carlo method; The probability formula for quantifying collapse pressure by combining the Monte Carlo method is:

[0058] 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.

[0059] Example In this embodiment, the relevant parameters involved in the hybrid multi-criteria collapse pressure probability quantification method based on GMM are from Well X as shown in Table 1 (the geomechanical parameter samples are also from Well X, see Figure 1 shown): Table 1 Geomechanical parameter data table

[0060] In this embodiment, the number of components obtained is K =7.

[0061] According to the above parameters, we can get Figure 1 The sampling data of geomechanical parameter samples obtained by using GMM combined with DBSCAN algorithm ( Figure 1 The scattered points in the figure represent the geomechanical parameter samples and sampling data, respectively), and Figure 2 The multi-criteria collapse pressure probability result of the wellbore obtained in the embodiment of the present invention is shown in FIG. Figure 2 The left curve in the middle is the probability density distribution of collapse pressure, and the shaded area corresponds to the high probability distribution area of ​​collapse pressure; the right curve is the reliability distribution curve of collapse pressure).

[0062] The embodiment of the present invention further provides a hybrid multi-criteria collapse pressure probability quantification system based on GMM, which is used to implement the hybrid multi-criteria collapse pressure probability quantification method based on GMM as described above, including: The geomechanical parameter sampling module of GMM combined with DBSCAN algorithm is 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 meets the uncertainty of geomechanical parameter samples; Hybrid multi-criteria collapse pressure probability quantification module: It is used to construct a wellbore stability evaluation model based on the wellbore stress distribution and different rock failure criteria, and realize the probability model calculation of wellbore collapse pressure by inputting probability weight coefficients.

[0063] The embodiments of the present invention also provide corresponding electronic devices and computer-readable storage media for implementing the solutions provided by the embodiments of the present invention.

[0064] 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-criteria collapse pressure probability quantification method described in any embodiment of the present application.

[0065] In practical applications, the computer-readable storage medium may be any combination of one or more computer-readable media, which may be a computer-readable signal medium or a computer-readable storage medium.

[0066] The above description is not intended to limit 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 technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are 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 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 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 based on the rock failure criterion; the above calculation process is repeated until N groups of sampling data are calculated.

10. 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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