Coal rock stratum heterogeneous permeability correlation random field unit sample generation method

Abstract

The invention discloses a shale reservoir heterogeneous porosity related random field unit sample generation method, and belongs to the technical field of coal mine underground space mining. Coal rock stratum heterogeneous permeability variability random field characterization is implemented, and coal rock stratum heterogeneous permeability local average random field unit characteristics and distributed random field unit samples are calculated; identifying an optimal probability density function of the heterogeneous permeability random field sample of the coal rock stratum; constructing a coal rock stratum heterogeneous permeability random field sample joint distribution function; calculating a sample mean value and covariance of a deep underground space stratum coal and rock mass heterogeneous permeability random field; and generating a random field unit sample related to the heterogeneous permeability of the coal rock stratum. By generating the random field unit sample related to the heterogeneous permeability of the coal rock stratum, the spatial variability and correlation characterization of the permeability of the coal rock stratum is realized, and an effective basis is provided for analyzing the permeability of the coal rock stratum in a coal mining process.

Description

Technical Field

[0001] This invention belongs to the field of underground space mining technology in coal mines, and particularly relates to a method for generating random field unit samples of heterogeneous permeability in coal and rock formations. Background Technology

[0002] The heterogeneity of permeability in coal and rock formations exhibits a dual pattern of vertical stratification and planar differentiation: vertically, controlled by sedimentary-diagenetic processes, permeability differences between different coal seams or even between laminae within the same coal seam can reach several to tens of times; planar, due to spatial differentiation of tectonic stress and sedimentary environment, interwoven heterogeneous fields often form, exhibiting significant directionality. During the primary depositional period of coal and rock, the lateral differences in the strength of hydrodynamics, source supply, and redox conditions in peat swamps laid the foundation for the initial heterogeneity of coal thickness, pore structure, and mineral composition. During tectonic activity, compression / tension caused coal and rock folding and fracturing, resulting in varying degrees of stress concentration in different regions, differentiation in the development density and connectivity of fracture networks, with high-stress areas experiencing fracture closure and impeded permeability, while low-stress areas saw fracture opening and increased permeability. Later fluid alteration further changed pore throats and mineral composition, superimposing and exacerbating heterogeneity. This heterogeneity makes the mechanical characteristics and seepage properties of coal and rock formations complex, affecting resource development efficiency. The random field method can scientifically and reasonably characterize the heterogeneous permeability of coal and rock formations, and the stochastic finite element method based on this model can be used to analyze the seepage mechanical stability of coal and rock masses.

[0003] However, to effectively integrate the characteristics of heterogeneous permeability in coal and rock formations into stochastic finite element analysis, it is necessary to discretize the permeability space random field to generate correlated locally averaged random field element samples. In the discretization process, the compatibility issue between the random field mesh and the finite element mesh is particularly prominent, significantly impacting computational accuracy and efficiency. The random field mesh is primarily used to characterize the distribution characteristics of spatial uncertainties, and its partitioning depends on the statistical properties and correlation length of random variables; while the finite element mesh is a discretization design for solving the physical field, dominated by factors such as structural geometry, load conditions, and boundary constraints. Due to the different partitioning criteria, the random field nodes and finite element nodes are often misaligned, ultimately making it difficult to directly map random field parameters to the finite element mesh. Furthermore, random field element samples generated by conventional methods often exhibit independent and identically distributed characteristics, making it difficult to effectively characterize the correlation between elements.

[0004] The prior art, disclosed in CN117390871A, describes a method for obtaining permeability of heterogeneous reservoirs based on inverse transform sampling, relating to the field of underground fluid seepage and heat transfer technology. The method includes: S1, acquiring geological data of the area to be measured, constructing a three-dimensional Cartesian coordinate system for the study area, determining the size and number of structural grids, the correlation distance lengths in each direction, and constructing a correlation matrix; S2, determining the number of random seeds and initially generating a random field using a random standard normal sequence; S3, determining the mean permeability and coefficient of variation of the study area; S4, performing inverse transform sampling on each structural grid; S5, importing the unstructured grid to obtain permeability data. This method simulates terrain distribution changes based on a random seed mechanism, requiring high initial information acquisition, significant computational power, and high operating costs. Summary of the Invention

[0005] Technical Problem: To address the shortcomings of existing technologies, this paper proposes a method for generating random field element samples of heterogeneous permeability in coal and rock formations that is computationally reliable, highly accurate, and easy for engineering designers to use. This method aims to solve the problem that existing random field parameters cannot be directly mapped to finite element meshes.

[0006] Technical Solution: To achieve the above objectives, this invention discloses a method for generating heterogeneous permeability-related random field unit samples in coal and rock formations, comprising the following steps: Step 1: Abstract the heterogeneous permeability properties of the coal and rock formation in a two-dimensional space into a stationary random field in a two-dimensional continuous space. Discretize the random field grid using six-node triangular units and number and label the generated six-node triangular random field units. Step 2: Using a six-node triangular random field unit, calculate the mean and covariance of any two discretized six-node triangular local average random field units; Step 3: Construct the global random field covariance matrix by taking the covariance of the local average random field units according to the unit numbering order. Calculate the eigenvector matrix and random vectors using the global random field covariance matrix, and finally calculate the random field unit samples that satisfy the independent and identical distribution of heterogeneous permeability in coal and rock formations. Step 4: The Gaussian Copula probability density function, Plackett Copula probability density function, and Clayton Copula probability density function are used to fit the random field unit samples that satisfy the independent and identical distribution of heterogeneous permeability in coal and rock formations, respectively. By comparing the fitting results of the three probability density functions, the optimal probability density function of the random field sample of heterogeneous permeability in coal and rock formations is identified. Step 5: Construct the joint distribution function of the random field sample of heterogeneous permeability in coal and rock formations using the optimal probability density function of the random field sample of heterogeneous permeability in coal and rock formations; Step 6: Calculate the mean value of the random field sample of heterogeneous permeability of coal and rock strata in deep underground space using the joint distribution function of the random field sample of heterogeneous permeability of coal and rock strata. Step 7: Calculate the sample covariance of heterogeneous permeability of coal and rock masses in deep underground strata using the mean and joint distribution function of the random field sample of heterogeneous permeability in deep underground coal and rock strata; Step 8: Assemble the matrix of the obtained random field covariance samples of heterogeneous permeability in coal and rock formations to obtain the overall random field covariance matrix. Repeat steps 3 to 7 to generate random field unit samples of heterogeneous permeability of coal and rock formations that meet the correlation conditions.

[0007] Furthermore, the calculation process for the characteristics of the locally averaged random field unit of heterogeneous permeability in coal and rock formations is as follows: Based on the statistical characteristics of the heterogeneous porosity random field in the two-dimensional space of coal and rock strata, the mean value of any two discretized six-node triangular local average random field elements is calculated using the following formula: , The covariance of any two discretized six-node triangular locally averaged random field elements can be calculated using the following formula: , , In the formula: , These are two random field units, , These are the coordinate differences between two random field units. , These are the areas of the two random field units, , These are the integration regions of two random fields, Let be the standard deviation of the random field. The correlation coefficient of a random field. , , , These are the coordinate values ​​of two random field units, respectively.

[0008] Furthermore, the steps for obtaining independent and identically distributed random field unit samples related to heterogeneous permeability are as follows: The local average random field covariance is matrix-assembled according to the cell numbering order to construct the global random field covariance matrix N; the eigenvector matrix L of matrix N is calculated, and a sequence of eigenvectors is generated. A normally distributed random variable is assigned to each six-node triangular random field unit, and the units are arranged in the order of their numbers to obtain the original random vector M. A new random vector K is generated by calculating the following formula, which is regarded as a single set of random field unit samples; , This process was repeated multiple times to obtain multiple sets of random field unit samples that satisfy the independent and identical distribution of heterogeneous permeability in coal and rock formations.

[0009] Furthermore, the steps for identifying the optimal probability density function for heterogeneous permeability random field samples in coal and rock formations are as follows: The correlation characteristics of heterogeneous permeability-correlated independent and identically distributed random field unit samples are described using the Gaussian Copula, Plackett Copula, and Clayton Copula probability density functions, respectively: The expression for the Gaussian Copula probability density function D1 is: , The expression for the Plackett Copula probability density function D2 is: , The expression for the Clayton Copula probability density function D3 is: , In the formula: u1 represents the random field unit sample in the horizontal direction, u2 represents the random field unit sample in the vertical direction, and θ represents the parameter related to the Copula function; The following formulas are used to calculate the fitting ability values ​​(THP) of the samples from heterogeneous permeability-related independent and identically distributed random field units, which describe the correlation characteristics of the Gaussian Copula, Plackett Copula, and Clayton Copula probability density functions, respectively. , The Copula probability density function that minimizes the THP value is the optimal probability density function. The selected optimal probability density function.

[0010] Furthermore, the joint distribution function of the random field sample of heterogeneous permeability in rock formations is calculated according to the following formula; , in , In the formula: This represents a sample of a random field unit in the horizontal direction within a two-dimensional space. This represents a vertical random field unit sample in a two-dimensional space. , Let p and q represent the marginal distribution functions of the random field samples of heterogeneous permeability in coal and rock formations, respectively, where p represents the mean of the random field unit and q represents the standard deviation of the random field unit. This represents the distribution function corresponding to the optimal probability density function.

[0011] Furthermore, the steps for calculating the mean of the random field sample of heterogeneous permeability of coal and rock masses in deep underground strata are as follows: The following formulas are used to calculate the random field sample mean of the heterogeneous permeability of coal and rock strata in deep underground spaces. , ; , .

[0012] Furthermore, the steps for calculating the sample covariance of heterogeneous permeability of coal and rock masses in deep underground strata are as follows: The following formula is used to calculate the sample covariance of heterogeneous permeability of coal and rock masses in deep underground strata; .

[0013] A sample data generation method using the heterogeneous permeability correlation random field unit sample generation method of coal and rock formations is used to conduct actual analysis on the data acquisition site to obtain highly consistent coal and rock permeability characteristics, thereby effectively analyzing the heterogeneous permeability of coal and rock formations and providing safety assurance for safe underground mining in coal mines.

[0014] A computer device, characterized in that it includes a processor and a memory, the processor being electrically connected to the memory, the memory being used to store instructions and data, and the processor being used to execute the method for generating random field unit samples of heterogeneous permeability in coal and rock formations.

[0015] Beneficial Effects: In this invention, both the heterogeneous permeability random field and the finite element structure of coal and rock formations are discretized using six-node triangular elements. They can directly share the same mesh system, with one-to-one correspondence between element numbers and clear logic, significantly simplifying the programming process. Compared to the mismatch between three-node triangular random field elements and six-node triangular finite element elements in traditional schemes, this design effectively avoids the mesh adaptation problem. This method can accurately construct random field element samples with correlation characteristics for heterogeneous permeability in coal and rock formations. The generated sample data can be directly applied to actual analysis scenarios, highly matching the real permeability characteristics of coal and rock, resulting in highly reliable calculation results. This sample generation method is not only applicable to the discretization analysis of heterogeneous permeability random fields in coal and rock formations, but also adaptable to the construction of random field element samples for other coal and rock permeability parameters (such as porosity and water content) with spatial variability and correlation characteristics, demonstrating strong technical universality. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the process of generating random field unit samples for heterogeneous permeability in coal and rock formations according to the present invention.

[0017] Figure 2 This is a stationary random field discretization diagram of heterogeneous permeability in coal and rock formations, as shown in a specific embodiment of the present invention.

[0018] Figure 3 This is a sample of independent and identically distributed random field units of permeability in coal and rock formations, representing a specific embodiment of the present invention.

[0019] Figure 4 This is a statistical feature diagram of the correlation random field of permeability in coal and rock formations, as shown in a specific embodiment of the present invention. Detailed Implementation

[0020] The following figures further illustrate embodiments of the present invention: This invention discloses a method for generating random field unit samples related to the heterogeneous permeability of coal and rock formations. The sample data generated by this method is used to conduct actual analysis of the data acquisition site, obtaining highly consistent coal and rock permeability characteristics. This effectively analyzes the heterogeneous permeability of coal and rock formations, providing a safety guarantee for safe underground coal mining. The specific steps are as follows: Step 1: Perform random field characterization of the permeability variability of heterogeneous coal and rock formations; The heterogeneous permeability properties of coal and rock formations within a two-dimensional spatial range are abstracted into a stationary random field form in a two-dimensional continuous space. The random field grid is discretized using six-node triangular units, and the generated six-node triangular random field units are numbered and identified.

[0021] Step 2: Calculate the local average random field element characteristics of heterogeneous permeability in coal and rock formations; Based on the statistical characteristics of the heterogeneous porosity random field in the two-dimensional space of coal and rock strata, the mean and covariance of any two discretized six-node triangular local average random field units are calculated using formulas (1) and (2): (1), , (2), In the formula: , These are two random field units, , These are the coordinate differences between two random field units. , These are the areas of the two random field units, , These are the integration regions of two random fields, Let be the standard deviation of the random field. The correlation coefficient of a random field. , , , These are the coordinate values ​​of two random field units, respectively.

[0022] Step 3: Obtain samples of heterogeneous permeability-related independent and identically distributed random field units; The covariance of the local average random field units is used to construct the overall random field covariance matrix according to the unit numbering order. The eigenvector matrix and random vector are calculated using the overall random field covariance matrix. Finally, random field unit samples that satisfy the independent and identical distribution of heterogeneous permeability in coal and rock formations are calculated. The local average random field covariance is matrix-assembled according to the cell numbering order to construct the global random field covariance matrix N; the eigenvector matrix L of matrix N is calculated, and a sequence of eigenvectors is generated. The distributed normal random variable is assigned to each six-node triangular random field unit, and arranged in the order of the six-node triangular random field unit number to obtain the original random vector M; the new random vector K is generated by formula (3) and regarded as a single set of random field unit samples; the process is repeated multiple times to obtain multiple sets of random field unit samples that satisfy the independent and identical distribution of heterogeneous permeability of coal and rock strata; (3).

[0023] Step 4: Identify the optimal probability density function for random field samples of heterogeneous permeability in coal and rock formations; The Gaussian Copula probability density function, Plackett Copula probability density function, and Clayton Copula probability density function were used to fit random field unit samples that satisfy the independent and identical distribution of heterogeneous permeability in coal and rock formations. The expression for the Gaussian Copula probability density function D1 is: , The expression for the Plackett Copula probability density function D2 is: , The expression for the Clayton Copula probability density function D3 is: , In the formula: u1 represents the random field unit sample in the horizontal direction, u2 represents the random field unit sample in the vertical direction, and θ represents the parameter related to the Copula function; The THP values, which describe the fitting ability of Gaussian Copula, Plackett Copula, and Clayton Copula probability density functions to the correlation characteristics of heterogeneous permeability-related independent and identically distributed random field unit samples, are as follows: (4), The Copula probability density function that minimizes the THP value is the optimal probability density function. The selected optimal probability density function.

[0024] Step 5: Construct the joint distribution function of random field samples of heterogeneous permeability in coal and rock formations; According to formula (5), the joint distribution function of random field samples of heterogeneous permeability in coal and rock formations is obtained; (5), In the formula: , These are the marginal distribution functions of the random field samples of heterogeneous permeability in coal and rock formations; The distribution function corresponding to the optimal probability density function; The marginal distribution function expression for a heterogeneous permeability random field sample is: .

[0025] Step 6: Calculate the mean value of random field samples of heterogeneous permeability of coal and rock masses in deep underground strata; Based on formulas (6) and (7), the mean values ​​of random field samples of heterogeneous permeability of coal and rock strata in deep underground space are calculated respectively; , .

[0026] Step 7: Calculate the sample covariance of heterogeneous permeability of coal and rock masses in deep underground strata; Based on formula (8), calculate the sample covariance of heterogeneous permeability of coal and rock masses in deep underground strata; (8).

[0027] Step 8: Generate random field unit samples related to the heterogeneous permeability of coal and rock formations; The covariance of the heterogeneous permeability random field samples of the obtained coal and rock formations is matrix-assembled to obtain the overall random field covariance matrix. Repeat step 3 to generate random field samples of heterogeneous permeability in coal and rock formations that meet the correlation conditions.

[0028] This method generates stochastic field unit samples related to the heterogeneous permeability of coal and rock formations, enabling the spatial variability and correlation characterization of permeability in these formations. This provides a valid basis for permeability analysis of coal and rock formations during coal mining. The stochastic field unit samples obtained by this method can be directly applied to stochastic finite element analysis calculations of permeability characteristics. The unit numbering correspondence is clear, the calculations are accurate, it is easy to program, and it has strong versatility.

[0029] Example: A two-dimensional cross-section of a deep coal and rock formation is square in shape, with heterogeneous spatial random field mean permeability. The value is 1.21 nD, and the standard deviation is 1.21 nD. The correlation coefficient is 0.11nD. Find 12 sets of random field unit samples related to the heterogeneous permeability of coal and rock formations.

[0030] Figure 2For the discrete case of a stationary random field representing the heterogeneous permeability of coal and rock strata, there are 8 random field elements. Nodes A, B, C, and D are used as the four corner nodes of the random field rectangle. The midpoint of line AB connecting nodes A and B is node E, the midpoint of line AE is node J, and the midpoint of line EB is node K; similarly, the midpoint of line BC is node F, the midpoint of line BF is L, the midpoint of line FC is M, the midpoint of line CD is G, the midpoint of line CG is N, the midpoint of line GD is P, the midpoint of line DA is H, and the midpoint of line DH is... Point Q is the midpoint of line HA, and I is the midpoint of line EG. Connecting the intersecting lines forms lines AC, BD, EG, and FH. The intersection of lines AC, BD, EG, and FH is node O. The midpoint of line OA is node R, the midpoint of line OB is node T, the midpoint of line OC is node V, the midpoint of line OD is node X, the midpoint of line OE is node S, the midpoint of line OF is node U, the midpoint of line OG is node W, and the midpoint of line OH is node Y. Table 1 shows the relationship between the element number and the node number. Table 1 ;

[0031] Figure 3 The process involved multiple implementations of 12 sets of independent and identically distributed random field unit samples of permeability in coal and rock formations to obtain multiple sets of independent and identically distributed random field unit samples (numbered 1# to 12#). After executing the process 12 times in step 3, multiple sets of random field unit samples satisfying the independent and identical distribution of permeability in heterogeneous coal and rock formations were obtained, resulting in 12 sets of independent and identically distributed random field unit samples. Figure 4 This is a statistical characteristic diagram of the random field related to the permeability of coal and rock formations, along with the sample mean and standard deviation. Figure 4 It can be seen that the total number of random field unit samples with independent and identically distributed permeability of the generated coal and rock strata is 96, with an average value of 1.226nD and a standard deviation of 0.116Nd.

[0032] Table 2 shows that 12 sets of heterogeneous permeability-related random field unit samples were generated from 8 random field units. In Table 2, the columns represent the random field unit numbers, the rows represent the group numbers, and the values ​​represent the heterogeneous permeability-related random field unit samples. Table 2 ;

[0033] The above description is only a preferred embodiment of the present invention. It should be noted that engineers and researchers in this field can make several improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for generating a coal rock formation heterogeneous permeability correlation random field unit sample, characterized in that: The method comprises the following steps: Step 1: Coal and rock formation heterogeneous permeability variability random field representation, using six-node triangular element implementation of random field grid discrete processing; Step 2: using six-node triangular random field unit, the mean and covariance of any two six-node triangular local average random field unit after discretization are calculated; Step 3: the covariance of the local average random field unit is constructed into the overall random field covariance matrix according to the sequence of the element number, the eigenvector matrix and the random vector are calculated by using the overall random field covariance matrix, and finally the random field unit sample satisfying the independent and identically distributed coal and rock formation heterogeneous permeability is calculated; Step 4: a plurality of probability density functions are used to fit the random field unit sample satisfying the independent and identically distributed coal and rock formation heterogeneous permeability, and the optimal probability density function of the coal and rock formation heterogeneous permeability random field sample is identified by comparing the fitting results of the plurality of probability density functions; Step 5: constructing the joint distribution function of the coal and rock formation heterogeneous permeability random field sample; Step 6: calculating the mean value of the coal and rock formation heterogeneous permeability random field sample in deep underground space; Step 7: calculating the sample covariance of the coal and rock formation heterogeneous permeability in deep underground space; Step 8: matrix assembly is performed on the obtained coal rock stratum heterogeneous permeability random field sample covariance to obtain an overall random field covariance matrix Steps 3 to 7 are repeated to generate a coal rock stratum heterogeneous permeability correlation random field unit sample that meets the correlation condition.

2. The method of claim 1, wherein, The feature calculation process of the local average random field unit of the coal and rock formation heterogeneous permeability is as follows: Based on the statistical characteristics of the heterogeneous porosity random field in the two-dimensional space range of the coal and rock formation, the mean value of any two six-node triangular local average random field units after discretization is calculated by using the following formula: ， The covariance of any two six-node triangular local average random field units after discretization is calculated by using the following formula: ， ， wherein: , are the coordinate difference values of the two random field units, , are the coordinate values of the two random field units, , are the areas of the two random field units, , are the integration regions of the two random fields, is the standard deviation of the random field, is the correlation coefficient of the random field, , , , are the coordinate values of the two random field units.

3. The method according to claim 2, wherein, The steps for obtaining the independent and identically distributed random field unit sample of the heterogeneous permeability are as follows: The local average random field covariance is sequentially performed matrix assembly according to the element number, and a whole random field covariance matrix N is constructed; a characteristic vector matrix L of the matrix N is calculated, and a normally distributed random variable assignment is generated arranged in the six-node triangular random field element number order, and an original random vector M is obtained. A new random vector K is generated by the following formula, which is regarded as a single set of random field unit samples; ， The process is executed multiple times to obtain multiple sets of random field unit samples satisfying the independent and identically distributed coal and rock formation heterogeneous permeability.

4. The method of claim 3, wherein, The steps for identifying the optimal probability density function of the coal and rock formation heterogeneous permeability random field sample are as follows: The independent and identically distributed random field unit sample of the heterogeneous permeability is described by using Gaussian Copula probability density function, Plackett Copula probability density function and Clayton Copula probability density function respectively to describe the correlation characteristics of the independent and identically distributed random field unit sample of the heterogeneous permeability: The expression of Gaussian Copula probability density function D1 is as follows: ， The expression of Plackett Copula probability density function D2 is as follows: ， The expression of Clayton Copula probability density function D3 is as follows: ， In the formula, u1 represents the horizontal direction random field unit sample, u2 represents the vertical direction random field unit sample, and θ represents the Copula function correlation parameter; The fitting capacity value THP of the correlation characteristics of the independent and identically distributed random field unit sample of the heterogeneous permeability described by Gaussian Copula probability density function, Plackett Copula probability density function and Clayton Copula probability density function respectively is calculated by using the following formula, ， The Copula probability density function with the minimum THP value is selected as the optimal probability density function, wherein is the selected optimal probability density function.

5. The method of claim 4, wherein, The joint distribution function of the heterogeneous permeability random field sample of the rock stratum is calculated according to the following formula: ， wherein , In the formula, represents the horizontal direction random field unit sample in the space in the two-dimensional space, represents the vertical direction random field unit sample in the space in the two-dimensional space; respectively represent the edge distribution functions of the coal rock stratum heterogeneous permeability random field sample, p represents the random field unit mean, and q represents the random field unit standard deviation; represents the distribution function corresponding to the optimal probability density function.​ 6. The method of claim 5, wherein, The step for calculating the mean value of the heterogeneous permeability random field sample of the coal rock mass of the deep underground space stratum is: The mean value of the heterogeneous permeability random field sample of the coal rock stratum of the deep underground space is calculated by using the following formula , ; ， 。 7. The method according to claim 6, wherein, The step for calculating the covariance of the heterogeneous permeability sample of the coal rock mass of the deep underground space stratum is: The covariance of the heterogeneous permeability sample of the coal rock mass of the deep underground space stratum is calculated by using the following formula: 。 8. A method for generating sample data of the coal rock stratum heterogeneous permeability related random field unit sample, the method comprising: using the sample data generated by the coal rock stratum heterogeneous permeability related random field unit sample generation method according to any one of claims 1-7 to perform actual analysis on a data collection site, obtaining highly consistent coal rock permeation information, and effectively analyzing the coal rock stratum heterogeneous permeation situation to provide safety guarantee for safe mining in a coal mine underground.

9. A computer device, comprising: The coal rock stratum heterogeneous permeability related random field unit sample generation method according to any one of claims 1-8 is executed by a processor and a memory, the processor is electrically connected with the memory, the memory is used for storing instructions and data, and the processor is used for executing the coal rock stratum heterogeneous permeability related random field unit sample generation method.

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