CN119885910B - Mixed multi-criterion collapse pressure probability quantification method based on GMM - Google Patents
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Abstract
The invention belongs to the technical field of deep stratum drilling and completion, and discloses a mixed multi-criterion collapse pressure probability quantification method based on GMM, which comprises the steps of collecting geomechanical parameter samples and performing standardized treatment; the method comprises the steps of carrying out cluster analysis on geomechanical parameter sample standardized data, constructing a parameter uncertainty quantization model by combining geomechanical parameter samples, constructing a well wall stability evaluation model according to well wall stress distribution and different rock breaking criteria, setting probability weight coefficients of different criterion models, randomly generating N groups of sampling data based on the parameter uncertainty quantization model, calculating well wall collapse pressure, and quantifying probability results of the collapse pressure by combining a Monte Carlo method. The invention can realize the quantification of the parameter high-dimensional joint probability distribution by using the geomechanical parameter sample, and further combines a plurality of damage criteria, so that a well wall multi-criterion collapse pressure probability model is constructed, thereby effectively improving the efficiency of the well wall collapse pressure uncertainty quantification work.
Description
Technical Field
The invention relates to a mixed multi-criterion collapse pressure probability quantification method based on GMM, and belongs to the technical field of oil-gas drilling and completion.
Background
The minimum drilling fluid column pressure required to maintain borehole wall stability is generally defined in the drilling engineering as the collapse pressure below which borehole wall rock tends to exhibit shear failure and further causes massive collapse of the borehole wall rock to severely interfere with safe performance of the drilling engineering.
At the same time, uncertainty characteristics of geological engineering severely interfere with accurate analysis of underground engineering and further cause parameter uncertainty and model uncertainty to interfere with quantification of borehole wall collapse pressure, and in particular, various rock failure criteria exist for borehole wall stability evaluation analysis, such as Mohr-Coulomb criteria, mogi-Coulomb criteria, modified Lade criteria, modified Wiebols-Cook criteria, and the like. Thus, the uncertainty quantization of the borehole wall collapse pressure is further exacerbated by the uncertainty of the geomechanical parameters and the ambiguity of the rock failure criteria selection.
At present, a theoretical calculation method of the collapse pressure of the well wall is carried out by a plurality of methods, for example, the invention patent with the authority number of CN114547906B of southwest petroleum university authorizes a well wall stable logging interpretation method of a deep stratum with a weak structural surface.
The invention patent of China Petroleum and Natural gas group Limited company and China Petroleum group Chuanqing drilling engineering Limited company grant number CN114635684B grants a well wall stability evaluation method and a well wall collapse pressure calculation method and system.
The two patents and other prior art schemes, although achieving certain technical effects, fail to fully consider the influence of geomechanical parameter uncertainty and rock failure criteria selection ambiguity, resulting in severely impeded quantification of borehole wall collapse pressure uncertainty in complex formations, thereby affecting implementation of underground drilling engineering.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a mixed multi-criterion collapse pressure probability quantification method based on GMM, and the method can utilize geomechanical parameter samples to realize quantification of parameter high-dimensional joint probability distribution, and further combine with various damage criteria to enable a well wall multi-criterion collapse pressure probability model to be constructed, so that the well wall collapse pressure uncertainty quantification work is effectively improved.
The invention provides a mixed multi-criterion collapse pressure probability quantification method based on GMM, which comprises the following steps:
Collecting geomechanical parameter samples according to logging data and indoor experimental results, and performing standardized treatment;
performing cluster analysis on geomechanical parameter sample standardized data by combining a DBSCAN algorithm to obtain a cluster number;
setting the number of components of the GMM model as a cluster number, and constructing a parameter uncertainty quantization model by combining geomechanical parameter samples;
Constructing a well wall stability evaluation model according to well wall stress distribution and different rock breaking criteria, and setting probability weight coefficients of different criterion models;
Randomly generating N groups of sampling data based on the parameter uncertainty quantization model, and calculating the collapse pressure of the well wall according to the probability weight coefficient;
And counting well wall collapse pressure calculation results under N groups of sampling data, and quantifying collapse pressure probability results by combining a Monte Carlo method.
Further technical solutions are that the geomechanical parameters include horizontal ground stress, overburden rock pressure, pore pressure, poisson's ratio, uniaxial compressive strength, cohesion and internal friction angle.
Further technical scheme is that the DBSCAN algorithm defines a cluster by defining a radius around a sample point, setting a minimum point number minPts, and calculating the number of data points in the radius.
The further technical scheme is that the theoretical formula of the DBSCAN algorithm is as follows:
Wherein: minPts is the minimum number of points, p and q are sample points; The Euclidean distance for sample points p, q; Is a radius.
The specific theoretical form of the GMM model is as follows:
Wherein: is a general form of n-dimensional gaussian distribution; is the mean vector of the kth Gaussian distribution; Covariance matrix of kth Gaussian distribution; k is the number of components of the GMM model; weight coefficient of kth Gaussian distribution, T is matrix Is a transpose of (a).
The further technical scheme is that the well wall stress distribution comprises:
Wherein: 、、、、、 Respectively radial effective stress, circumferential effective stress, axial effective stress of surrounding rock of a cylindrical coordinate system, Plane shear stress,Plane shear stressPlane shear stress, MPa;、、、、、 respectively is Directional effective stress,Directional effective stress,Directional effective stress,Plane shear stress,Plane shear stressPlane shear stress, MPa; the pressure is the liquid column pressure of the drilling fluid and MPa; The pore pressure is MPa, v is Poisson's ratio, and the pore pressure is dimensionless; is the fracture angle, degree around the well.
Further technical solutions are that the different rock breaking criteria include the Mohr-Coulomb criterion, modified Lade criterion, modified Wiebols-Cook criterion and Mogi-Coulomb criterion.
The further technical scheme is that the well wall stability evaluation model comprises two parts of well wall stress distribution and a rock failure criterion, and the minimum well wall drilling fluid density is solved and maintained as well wall collapse pressure by substituting the well wall stress distribution into the rock failure criterion.
The further technical scheme is that the process for calculating the collapse pressure of the well wall according to the probability weight coefficient comprises the following steps:
Generating random numbers r in the intervals [0,1], comparing the random numbers r with the sum of probability weight coefficients of different numbers of rock breaking criteria one by one until the random numbers r are larger than the sum of the probability weight coefficients, outputting the number l of the rock breaking criteria, correspondingly selecting the first rock breaking criteria to calculate collapse pressure, and repeating the calculation process until N groups of sampling data are calculated.
The further technical scheme is that the probability formula for quantifying collapse pressure by combining the Monte Carlo method is as follows:
Wherein: Probability of collapse pressure; Pressure equal to collapse in sample set Is the number of (3); Is the total number of samples; is the interval width.
The invention also provides an electronic device, comprising:
One or more processors;
A storage device having one or more programs stored thereon;
The one or more programs, when executed by the one or more processors, cause the one or more processors to implement the GMM-based hybrid multi-criterion collapse pressure probability quantification method of the present invention as described above.
The invention also provides a storage medium having stored thereon a computer program which, when executed by a processor, implements the GMM-based hybrid multi-criterion collapse pressure probability quantification method of the invention as described above.
The GMM-based mixed multi-criterion collapse pressure probability quantification method has the advantages that the GMM-based mixed multi-criterion collapse pressure probability quantification method is used for collecting geomechanical parameter samples and combining a DBSCAN algorithm to predict the number of components of a mixed Gaussian probability model, the GMM is further used for realizing the geomechanical parameter uncertainty quantification under the conditions of correlation characteristics and complicated distribution, and the multi-criterion well wall collapse pressure probability model construction under the conditions of geomechanical parameter uncertainty is realized by determining weight coefficients under different criteria. The invention considers the relativity and uncertainty influence of the geomechanical parameters of the reservoir, and provides theory and technical guidance for the uncertainty analysis of the collapse pressure of the well wall through the combination of the GMM and the DBSCAN.
Drawings
FIG. 1 is a sample data of a geomechanical parameter sample obtained by using GMM in combination with DBSCAN algorithm (base data source: X-well) according to an embodiment of the present invention;
FIG. 2 is a graph of the borehole wall multi-criteria collapse pressure probability results (base data source: X-well) obtained in an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention discloses a mixed multi-criterion collapse pressure probability quantification method based on GMM, which comprises the following steps:
Step one, collecting geomechanical parameter samples according to logging data and indoor experimental results, and performing standardization processing to obtain geomechanical parameter sample standardization data;
Wherein 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 of the normalization process is as follows:
Wherein: Is an original geomechanical parameter sample; is the geomechanical parameter sample mean value; standard deviation is a geomechanical parameter sample; is normalized sample data;
Step two, clustering analysis is carried out on geomechanical parameter sample standardized data by combining a DBSCAN algorithm to obtain a clustering number;
Wherein the DBSCAN algorithm is implemented by defining a radius around the sample point Setting the minimum point number minPts, and calculating the radius againThe number of data points within to define the cluster.
The theoretical formula of the DBSCAN algorithm is as follows:
Wherein: minPts is the minimum number of points, p and q are sample points; The Euclidean distance for sample points p, q; Is a radius;
Step three, setting the number of components of the GMM model as a cluster number, and constructing a parameter uncertainty quantization model by combining geomechanical parameter samples;
the specific theoretical form of the GMM model (gaussian mixture model) is:
Wherein: is a general form of n-dimensional gaussian distribution; is the mean vector of the kth Gaussian distribution; Covariance matrix of kth Gaussian distribution; k is the number of components of the GMM model; weight coefficient of kth Gaussian distribution, T is matrix Is a transpose of (2);
Wherein the method comprises the steps of The following conditions are satisfied:
step four, constructing a well wall stability evaluation model according to well wall stress distribution and different rock breaking criteria, and setting probability weight coefficients of different criterion models;
Wherein the borehole wall stress distribution comprises:
Wherein: 、、、、、 Respectively radial effective stress, circumferential effective stress, axial effective stress of surrounding rock of a cylindrical coordinate system, Plane shear stress,Plane shear stressPlane shear stress, MPa;、、、、、 respectively is Directional effective stress,Directional effective stress,Directional effective stress,Plane shear stress,Plane shear stressPlane shear stress, MPa; the pressure is the liquid column pressure of the drilling fluid and MPa; The pore pressure is MPa, v is Poisson's ratio, and the pore pressure is dimensionless; angle, degree, for periwell damage;
The in-situ stress field variable in the rectangular coordinate system of the well bore is obtained by the following relation:
Wherein: is the horizontal maximum ground stress, MPa; is the horizontal minimum ground stress, MPa; The pressure of the overburden rock is MPa, and w is the included angle between the maximum ground stress and the azimuth angle of the well bore; Is a well bevel;
The rock failure criteria include Mohr-Coulomb criteria, modified Lade criteria, modified Wiebols-Cook criteria, mogi-Coulomb criteria;
wherein Mohr-Coulomb criterion:
the Mohr-Coulomb criterion, ignoring the effects of intermediate stresses, considers that rock failure results from the shear stress at the shear plane overcoming the sum of the inherent cohesion of the rock and the friction at the shear plane, namely:
wherein, the uniaxial compressive strength of sigma c rock is MPa, and psi is internal friction angle.
Modified Lade criterion:
Wherein: 、、 Is the first, second and third effective principal stress, MPa, S, eta are material constants depending on cohesion and internal friction angle, C o is rock cohesion, MPa;
Modified Wiebols-Cook criterion:
wherein the coefficients A, B and C can be obtained by the following relationship:
Wherein: the primary stress is the first invariant, MPa; the stress deflection is the second invariant, MPa; the stress deflection is the first invariant, MPa; the coefficient is related to the rock strength, and the coefficient is related to the cohesive force;
Mogi-Coulomb criterion:
Wherein: Is the shear stress of a regular octahedron and MPa; the average positive stress is MPa, and a and b are coefficients related to materials.
Probability weight coefficientThe larger the value representing the probability of selection of a rock failure criterion, the higher the likelihood of application of that criterion, where m represents the total number of rock failure criteria and satisfies the sum of all weighting coefficients to be 1;
the well wall stability evaluation model is used for solving and maintaining the minimum well wall drilling fluid density as well wall collapse pressure through substituting well wall stress distribution into a rock breaking criterion;
Step five, randomly generating N groups of sampling data based on a parameter uncertainty quantization model, and calculating the collapse pressure of the well wall according to a probability weight coefficient;
The process for calculating the collapse pressure of the well wall according to the probability weight coefficient comprises the steps of generating random numbers r in intervals [0,1], and utilizing the random numbers r to be added with the probability weight coefficients of different numbers of rock breaking criteria one by one Comparing until the random number r is greater than the sum of the probability weight coefficientsOutputting the number of rock breaking criteria, selecting the first rock breaking criteria to calculate collapse pressure, repeating the calculation until N groups of sampling data are calculated.
Step six, counting well wall collapse pressure calculation results under N groups of sampling data, and quantifying collapse pressure probability results by combining a Monte Carlo method;
the probability formula for quantifying collapse pressure by combining the Monte Carlo method is as follows:
Wherein: Probability of collapse pressure; Pressure equal to collapse in sample set Is the number of (3); Is the total number of samples; is the interval width.
Examples
In this embodiment, the relevant parameter source X-well related to the GMM-based hybrid multi-criterion collapse pressure probability quantification method is shown in table 1 (geomechanical parameter samples are also derived from the X-well, see fig. 1):
table 1 geomechanical parameter data sheet
In this embodiment, the number of obtained components is k=7.
According to the parameters, sampling data of a geomechanical parameter sample obtained by using the GMM combined with the DBSCAN algorithm shown in FIG. 1 (scattered points in FIG. 1 represent the geomechanical parameter sample and the sampling data respectively), and a well wall multi-criterion collapse pressure probability result obtained in the embodiment of the invention shown in FIG. 2 (left side curve in FIG. 2 is collapse pressure probability density distribution, shadow area corresponds to collapse pressure high probability distribution area, and right side curve is collapse pressure reliability distribution curve).
The embodiment of the invention also provides a mixed multi-criterion collapse pressure probability quantification system based on the GMM, which is used for realizing the mixed multi-criterion collapse pressure probability quantification method based on the GMM, and comprises the following steps:
the GMM combined DBSCAN algorithm geomechanical parameter sample sampling module is used for analyzing uncertainty characteristics of a current geomechanical sample and constructing a high-dimensional joint probability distribution function meeting the uncertainty characteristics, so that data sampling conforming to the uncertainty of the geomechanical parameter sample is further realized;
and the mixed multi-criterion collapse pressure probability quantification module is used for constructing a well wall stability evaluation model according to well wall stress distribution and different rock destruction criteria, and realizing probability model calculation of the well wall collapse pressure by inputting probability weight coefficients.
The embodiment of the invention also provides corresponding electronic equipment and a computer readable storage medium, which are used for realizing the scheme provided by the embodiment of the invention.
The electronic equipment comprises a storage device and a processor, wherein the storage device is used for storing instructions or codes, and the processor is used for executing the instructions or codes so that the electronic equipment can execute the mixed multi-criterion collapse pressure probability quantification method based on the GMM according to any embodiment of the application.
In practical applications, the computer-readable storage medium may take the form of any combination of one or more computer-readable media. The computer readable medium may be a computer readable signal medium or a computer readable storage medium.
The present invention is not limited to the above-mentioned embodiments, but is not limited to the above-mentioned embodiments, and any person skilled in the art can make some changes or modifications to the equivalent embodiments without departing from the scope of the technical solution of the present invention, but any simple modification, equivalent changes and modifications to the above-mentioned embodiments according to the technical substance of the present invention are within the scope of the technical solution of the present invention.
Claims (9)
1. The mixed multi-criterion collapse pressure probability quantification method based on the GMM is characterized by comprising the following steps of:
Collecting geomechanical parameter samples according to logging data and indoor experimental results, and performing standardized treatment;
performing cluster analysis on geomechanical parameter sample standardized data by combining a DBSCAN algorithm to obtain a cluster number;
setting the number of components of the GMM model as a cluster number, and constructing a parameter uncertainty quantization model by combining geomechanical parameter samples;
Constructing a well wall stability evaluation model according to well wall stress distribution and different rock breaking criteria, and setting probability weight coefficients of different criterion models;
Randomly generating N groups of sampling data based on the parameter uncertainty quantization model, and calculating the collapse pressure of the well wall according to the probability weight coefficient;
the process for calculating the collapse pressure of the well wall according to the probability weight coefficient comprises the following steps:
Generating random numbers r in the intervals [0,1], comparing the random numbers r with the sum of probability weight coefficients of rock failure criteria with different numbers one by one until the random numbers r are larger than the sum of the probability weight coefficients, outputting the number l of the rock failure criteria, and correspondingly selecting the first rock failure criterion to calculate collapse pressure;
And counting well wall collapse pressure calculation results under N groups of sampling data, and quantifying collapse pressure probability results by combining a Monte Carlo method.
2. The GMM-based hybrid multi-criterion collapse pressure probability quantification method of claim 1, wherein 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 GMM-based hybrid multi-criteria collapse pressure probability quantization method of claim 1, wherein the DBSCAN algorithm defines clusters by defining a radius around the sample points and setting a minimum number minPts of points, and calculating the number of data points within the radius.
4. The GMM-based hybrid multi-criterion collapse pressure probability quantization method according to claim 3, wherein the theoretical formula of the DBSCAN algorithm is:
Wherein: minPts is the minimum number of points, p and q are sample points; The Euclidean distance for sample points p, q; Is a radius.
5. The GMM-based hybrid multi-criterion collapse pressure probability quantification method of claim 1, wherein the specific theoretical form of the GMM model is:
Wherein: is a general form of n-dimensional gaussian distribution; is the mean vector of the kth Gaussian distribution; Covariance matrix of kth Gaussian distribution; k is the number of components of the GMM model; weight coefficient of kth Gaussian distribution, T is matrix Is a transpose of (a).
6. The GMM-based hybrid multi-criteria collapse pressure probability quantification method of claim 1, wherein the borehole wall stress distribution comprises:
Wherein: 、、、、、 Respectively radial effective stress, circumferential effective stress, axial effective stress of surrounding rock of a cylindrical coordinate system, Plane shear stress,Plane shear stressPlane shear stress, MPa;、、、、、 respectively is Directional effective stress,Directional effective stress,Directional effective stress,Plane shear stress,Plane shear stressPlane shear stress, MPa; the pressure is the liquid column pressure of the drilling fluid and MPa; The pore pressure is MPa, v is Poisson's ratio, and the pore pressure is dimensionless; is the fracture angle, degree around the well.
7. The GMM-based hybrid multi-criterion collapse pressure probability quantification method of claim 1, wherein the different rock failure criteria include a Mohr-Coulomb criterion, modified Lade criterion, modified Wiebols-Cook criterion, and Mogi-Coulomb criterion.
8. The method for quantifying the probability of collapse of a mixed multi-criterion based on GMM according to claim 1, wherein the well wall stability evaluation model comprises two parts of well wall stress distribution and a rock failure criterion, and the minimum well drilling fluid density of the well wall is solved and maintained as the well wall collapse pressure by substituting the well wall stress distribution into the rock failure criterion.
9. The GMM-based mixed multi-criterion collapse pressure probability quantification method according to claim 1, wherein the probability formula for quantifying the collapse pressure in combination with the monte carlo method is:
Wherein: Probability of collapse pressure; Pressure equal to collapse in sample set Is the number of (3); Is the total number of samples; is the interval width.
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