Karst reservoir geometric heterogeneity evaluation method based on continuous coherence theory

Abstract

The invention discloses a karst reservoir geometric heterogeneity evaluation method based on a continuous coherence theory, and the method comprises the steps: obtaining a rock sample pore image through a tomography technology, converting the spatial distribution of a pore body into sphere cloud data, and constructing a Rips complex through the continuous coherence theory, the birth time and the death time of the topological features of the data set are captured, then the duration of the topological features is calculated and output to obtain a PD graph, and probability density function weighted average is applied to determination of the PD mass center; and then the complexity and heterogeneity of the reservoir pore structure are quantified and represented by calculating the mean value and variance of the duration, the higher the mean value and variance are, the higher the heterogeneity of the rock pore structure is, and the proposed heterogeneity quantitative index H verifies that the analysis index has reasonability. According to the method, the quantitative evaluation capability of the heterogeneity of the pore structure of the geological reservoir is improved, and assistance is provided for research and production in the field of karst reservoirs.

Description

Technical Field

[0001] The present invention relates to the technical field of geological exploration engineering, and particularly relates to a method for evaluating the geometric heterogeneity of karst reservoirs based on persistent homology theory. Background Art

[0002] The geometric heterogeneity of geological reservoirs refers to the non-uniformity of the spatial distribution of reservoir pore structures, and this characteristic is crucial for predicting the transport properties (e.g., permeability and conductivity) and elastic properties of reservoirs. The geometric shapes of naturally formed rock pores have significant heterogeneity, which is significantly different from the characteristics of artificial materials, thus increasing the difficulty of predicting their rock physical properties. The pore structure heterogeneity of reservoirs directly affects key parameters such as fluid permeability, connectivity, and elastic modulus, and these parameters have a decisive impact on oil and gas exploration and production (Pun, C. S., Lee, S. X., & Xia, K. (2022). Persistent-homology-based machine learning: A survey and a comparative study. Artificial Intelligence Review, 55(7), 5169–5213. https: / / doi.org / 10.1007 / s10462-022-10146-z).

[0003] Traditional pore structure evaluation methods, such as porosity, permeability, pore size distribution, and connectivity number, although they can provide a certain degree of structural information, lack the analysis of the spatial combination structure information of pore structures. In recent years, the persistent homology theory in Topology Data Analysis (TDA) has been introduced into the characterization of rock pore geometric features, providing a new method for evaluating pore heterogeneity. TDA is a data analysis method that combines topology, algebra, geometry, and data analysis techniques to analyze the topological features of data sets. In topology, geometric objects or spatial structures often retain some invariant features after changing relative distances and position relationships, and these are called topological invariants. And TDA is exactly the method used to capture such quantities to reveal the essence of the research object (Jiang F, Tsuji T, Shirai T. Pore geometry characterization by persistent homology theory[J]. Water Resources Research, 2018, 54(6): 4150-4163).

[0004] Persistent homology theory, as one of the main contents of TDA, is a mathematical tool for analyzing the topological features of a dataset. It can obtain topological features in high-dimensional datasets. Compared with traditional topological models, the advantage of the persistent homology model is that it is a multi-scale representation. Through the idea of filtration, it avoids the defect of only retaining the inherent structural information in traditional topology. Data at different scales have different structures and patterns. For example, the geomorphic features in geographical data can be observed at different scales. For each scale, a simplicial complex is constructed according to different parameters (such as radius) and the persistent homology is calculated, which represents the topological features found at a specific scale. After persistent homology analysis, the topological features of the dataset are obtained, thereby revealing the structure and characteristics of the data (Bizhani M, Haeri Ardakani O. Pore Characterization of Organic-Rich Shales through Application of Topological Data Analysis and Persistent Homology[J]. Energy&Fuels, 2021, 35(22): 18563-18573).

[0005] However, when the existing persistent homology theory is applied to the pore structure of rocks, the following main deficiencies exist: Although it can extract topological features, the description of the spatial distribution and connectivity of the pore structure is not detailed enough, unable to comprehensively reflect the geometric heterogeneity of the pores and lacking an intuitive and accurate quantitative index to evaluate the heterogeneity of the pore structure, resulting in poor comparability and practicability of the evaluation results.

[0006] The present invention aims to solve the above deficiencies in the prior art. By preliminarily analyzing the mean and variance of the persistence - birth time diagram to qualitatively analyze the information of reservoir heterogeneity, and comparing the results with a dimensionless heterogeneity quantification index H proposed in relevant literature (Jiang F, Tsuji T, Shirai T. Pore geometry characterization by persistent homology theory[J]. Water Resources Research, 2018, 54(6): 4150-4163), the heterogeneity of the rock pore structure is evaluated intuitively and accurately. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for evaluating the geometric heterogeneity of karst reservoirs based on persistent homology theory. This method is particularly applicable to geological reservoirs, especially karst reservoirs, and can more accurately describe and quantify the heterogeneity of the rock pore structure.

[0008] To achieve the above object, the present invention provides the following technical solutions and general steps: micro-computed tomography, binarization, pore network extraction, persistent homology theory analysis, persistence diagram (PD diagram) plotting, calculation of mean and variance of duration, calculation of heterogeneity quantification index H, specifically as follows.

[0009] The present invention provides a method for evaluating the geometric heterogeneity of a karst reservoir, comprising the following steps: (1) Performing micro-computed tomography on a karst reservoir sample to obtain a three-dimensional CT image of its internal pore structure; (2) Performing binarization on the CT image, and using image segmentation technology to divide the pixel points in the image into a background representing pores and a foreground representing minerals; (3) On the basis of the binarized image, applying a pore network extraction algorithm to extract the spatial distribution information of pore bodies from the binarized image, and constructing the largest sphere in the pore space. The center point and radius information of the sphere constitute the sphere cloud data representing the pore body; (4) Analyzing the extracted sphere cloud data using persistent homology theory analysis to calculate the persistence PD diagram; (5) Calculating the heterogeneity quantification index H from the persistence diagram. The lower the value of the index H, the higher the heterogeneity of the rock pore structure.

[0010] Preferably, the above karst reservoir sample includes pore-fracture type, pore-cavity type and intercrystalline pore type karst reservoirs.

[0011] Preferably, the above binarization is performed by applying an adaptive threshold algorithm to automatically determine the threshold according to the local statistical characteristics of the image, so as to improve the discrimination accuracy and accurately distinguish the pore space and mineral matrix of the rock sample.

[0012] Preferably, the above pore network extraction algorithm can be selected from the largest sphere algorithm.

[0013] Preferably, the persistent homology theory analysis in the above evaluation method is specifically as follows: (1) Constructing a Rips complex by considering the distance between data points; (2) Capturing and recording the topological features of the data set, including the time when the topological feature starts to appear as the birth time birth and the time when it disappears as the death time birth, to obtain the duration of each topological feature; (3) Visualizing the topological features through the persistence PD diagram to represent the spatial distribution of pore bodies.

[0014] Preferably, in the above persistent homology theory analysis, the construction of the Rips complex takes into account the geometric distance between data points, and the radius of the sphere is used as the filtering parameter ε, whose value continuously increases from 0 to obtain an image of the birth and death of topological model features, ensuring the comprehensive capture of topological features.

[0015] Preferably, in the above evaluation method, the persistence diagram is drawn based on the core density prediction algorithm, and its density calculation formula is shown in Equation (1); Equation (1) where: is the probability density value of this topological feature point; is the total number of sample data points; is a data point with multiple dimensions in the sample data, or a vector, where each dimension corresponds to the value of the data point on different features or attributes, and the coordinates in persistent homology are , where b is the birth time and d is the death time; is the Gaussian kernel function, indicating the kernel function related to the data point with bandwidth The expression of the Gaussian kernel function is: Equation (2) where, is a variable, indicating the distance between and the data point , that is ; is the bandwidth, which is used to control the width of the kernel function and determines the smoothness of the estimation.

[0016] Preferably, in the above persistence diagram, the duration of each topological feature is calculated by subtracting the birth time from the death time, and the topological features with a duration greater than the preset threshold are identified as signals, and the rest are noise, which may introduce false topological features to interfere with the true features due to the randomness and uncertainty in the data; among them, data smoothing and noise processing methods are used to handle the noise.

[0017] Preferably, in the above evaluation method, the statistical parameters describing the topological feature distribution in the persistence PD diagram are the mean and variance of the duration, which provide quantitative information for the heterogeneity of the reservoir pore structure.

[0018] Preferably, in the above evaluation method, the calculation formula of the heterogeneity quantification index H is shown in Equation (3): Equation (3) where, and are the distances from the centroid to the PD diagonal and the death axis, It is the lifespan of the longest lifespan point in PD, which is used for normalization to ensure the comparability of H values.

[0019] The present invention has the following advantages: The present invention calculates a persistence diagram (PD) from a point cloud, and based on the PD, applies a weighted average of probability density functions to the determination of the centroid, extracts the heterogeneous characteristics of the reservoir from the duration mean and variance, and finally combines the persistence diagram with the index H related to quantifying heterogeneity for result comparison. This method provides an intuitive, accurate and reliable means to evaluate the heterogeneity of the pore structure of rocks and has important practical application value.

[0020] The method of the present invention provides a new perspective and tool for evaluating the geometric heterogeneity of geological reservoirs, helps to deeply understand the physical properties of reservoirs, and has theoretical and practical significance for oil and gas exploration and development. Brief Description of the Drawings

[0021] Figure 1 It is a schematic diagram after CT scanning of three types of rocks: pore-fracture type, vuggy type, and intercrystalline pore type.

[0022] Figure 2 It is a schematic diagram of the sphere cloud filtering process in the present invention.

[0023] Figure 3 It is a schematic diagram of the persistence after strengthening a certain persistent feature in the present invention.

[0024] Figure 4 It is the result of the PD diagram of pore-fracture type rock and the calculated H value.

[0025] Figure 5 It is the result of the PD diagram of vuggy type rock and the calculated H value.

[0026] Figure 6 It is the result of the PD diagram of intercrystalline pore type rock and the calculated H value. Detailed Description of the Preferred Embodiments

[0027] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0028] Note: The experimental methods in the following embodiments are all conventional methods unless otherwise specified, and are carried out according to the techniques or conditions described in the literature in this field or according to the product specifications. The materials, reagents, etc. used in the following embodiments can be obtained from commercial channels unless otherwise specified.

[0029] Example 1 This example provides a method for evaluating the geometric heterogeneity of karst reservoirs based on persistent homology theory. This method is particularly applicable to geological reservoirs, especially karst reservoirs, and can more accurately describe and quantify the heterogeneity of rock pore structures. It will be described in detail with reference to the accompanying drawings as follows:

[0030] First, high-precision micro-computed tomography (micro-CT) technology is used to carefully scan rock samples to obtain three-dimensional images of their internal pore structures. The scanning conditions of three different rock samples are obtained, namely pore-fracture type (a), vuggy type (b), and intercrystalline pore type (c), as shown specifically in Figure 1 the figure, where black represents the rock skeleton and the transparent color represents the pore space. This step is the basis for subsequent analysis, ensuring the resolution and quality of the image, and providing a guarantee for accurately reflecting the fine characteristics of rock pores.

[0031] The obtained CT images are then binarized. This process uses image segmentation technology to divide the pixel points in the image into the background representing pores and the foreground representing minerals. This step accurately distinguishes the pore space and mineral matrix of the rock by applying a threshold algorithm, laying the foundation for the extraction of the pore network.

[0032] Based on the binarized image, a pore network extraction algorithm, such as the largest ball algorithm, is used to extract the spatial distribution information of pore bodies from the image. This step involves constructing the largest spheres within the pore space, and the center point and radius information of these spheres constitute the sphere cloud data representing pore bodies, providing key input for subsequent persistent homology analysis.

[0033] Then, the persistent homology theory is used to deeply analyze the extracted sphere cloud data, and the persistence diagram (PD) is calculated. PD can reveal the topological characteristics of the spatial distribution of pore bodies, such as connectivity, the presence and changes of loops and cavities, thus providing a new perspective for evaluating the complexity of pore structures.

[0034] First, the complex pore geometry is represented as sphere cloud data using the pore network extraction method. The same point cloud data generates different simple complexes under different rules. The Rips complex is used here. The Rips complex is constructed by considering the distance between data points to capture the topological features of the data set. Its construction is based on a radius parameter, which is used to determine which data points are connected. Each point in the data set is associated with a sphere of the same size, and the sphere radius is used as a filtering parameter. The key to the whole process lies in the setting of the filtering parameter ε. By increasing ε from 0 to a maximum value that makes the whole a huge simplex, an image of the topological model features from birth to death will be obtained. The time when a topological feature begins to appear is recorded as birth, and the time when it disappears is recorded as death. The duration of each topological feature is thus obtained. Features that can be maintained for a longer time are defined as signals. The duration of these invariants is directly related to the geometric properties, that is, the quantity to be explored. Features with a very short lifespan are called noise. Usually refers to the randomness and uncertainty in the data, which may introduce false topological features to interfere with the real features. To this end, noise must be handled with caution, and methods such as data smoothing and noise processing are often used. The whole process is called continuous coherence.

[0035] For details, please refer to the attached Figure 2 , represented as a schematic diagram of spherical cloud filtering, which uses the sphere radius As a filter parameter. As the value increases from 0, we will find that the topological characteristics are constantly changing. This provides a concise way to describe the overall picture of the data, indicating how many clusters, ring structures, and topological structures there are in the data. Figure 2 In such a two-dimensional point cloud data, when , it looks like just a series of points placed in space with no apparent relationship. As the radius of each center point increases, intersections begin to appear between different points. When the red topological ring structure begins to form, as it continues to grow, blue and green topological structures appear. By capturing this information, it is plotted in the birth-death diagram. Figure 2 B in the figure; different topological features have different durations, among which The red feature that appears at the time of birth lasts the longest and is represented by The point is farthest from the diagonal line, which provides theoretical support for subsequent analysis.

[0036] After obtaining the topological features of the dataset through persistent homology analysis, the next step is to visualize it. The visualization results of PH are generally Persistent Diagrams (PDs), Persistent Barcodes (PBs), etc. A Persistent Diagram (PD) is a two-dimensional histogram obtained by using the birth and death times of each point recorded during the filtration process as the coordinates of the point (birth, b ; death, d ). This chart represents the spatial distribution of pore bodies.

[0037] The drawing of the Persistent Diagram is based on the Kernel Density Estimation (KDE) algorithm. This is a non-parametric statistical method for estimating the Probability Density Function (PDF). KDE is a technique that forms a smooth density estimate by placing kernel functions around each data point and then performing a weighted sum of these kernel functions. The mathematical expression for the calculation method is as follows:

[0038] where, is the probability density value of the point; is the total number of sample data points; is a data point with multiple dimensions in the sample data, or a vector, where each dimension corresponds to the value of the data point on different features or attributes. In persistent homology, it is the coordinate . is the Gaussian kernel function, representing the kernel function related to the data point , with a bandwidth The expression of the Gaussian kernel function is:

[0039] where, is a variable representing the distance between the data point and, that is, ; is the bandwidth, which is used to control the width of the kernel function and determines the smoothness of the estimate.

[0040] By applying the Gaussian kernel function to the sample data points and performing a weighted sum, the estimated density values at different data points can be obtained, constructing an estimate of the entire probability density function. Then, the centroid is obtained by taking the weighted average of the probability density of each point. The specific expression is as follows: where: is the coordinate of the centroid; is the number of points in the persistence diagram; is the coordinate of the th point in the persistence diagram, representing the appearance time and the death time; weight of the th point, which here refers to the probability density of this point, i.e., ; It is not necessary to only select the probability density. When the probability density is selected, the determined centroid should be consistent with the point with the darkest color in the PD diagram. It should also be possible to select the length of the duration as the weight ; in this case, the obtained centroid is measured by the duration. That is, different importances are assigned to each point, and the centroid obtained by weighted average can be regarded as reflecting the overall topological properties.

[0041] After obtaining the PD diagram, other processing can also be performed on it to enhance certain persistent features. Here, first, a linear transformation is applied to all its points, changing T(x, y) to T(x, y - x), that is, the survival-death coordinates become survival-duration coordinates. The advantage of implementing this transformation is to expand the region that only exists above the diagonal to the entire coordinate, which is convenient for observation and at the same time emphasizes its persistent features more. To highlight the features of a certain point in the entire dataset, the following operations are performed to strengthen the influence of its position and features.

[0042] 1. Centralize the probability distribution of each point in the persistence diagram. Commonly used is the normalized multivariate Gaussian distribution. It has excellent properties: it satisfies the central limit theorem. When the amount of data is large, the distribution of any set of data is close to the Gaussian distribution.

[0043] When the Gaussian formula determines and , its form is fixed. Here, the coordinates of a certain point are selected as , where is the standard deviation of this distribution, which is set according to the needs of the dataset. When is larger, the form of the Gaussian distribution is flatter, that is, the influence range of this point on the surrounding is larger. When is smaller, the form of the Gaussian distribution is more "sharp", that is, the influence range of this point on the surrounding is smaller. In this way, the corresponding probability distribution is obtained from a certain point. It describes the distribution situation near this point. The probability of this point is the largest, and the closer the distance to this point, the greater the probability. Record this probability distribution as . Repeat the above operation to traverse each point in the dataset. The number of probability distributions obtained can be the same as the number of points.

[0044] 2. Perform a weighted operation on the probability distribution corresponding to each point. Weighting is to artificially highlight a desired feature. The most flexible part of this operation is the choice of weighting function, which is mainly used to adjust the importance of a feature.

[0045] It is a arrive A linear transformation maps the two-dimensional space into one dimension, which will greatly reduce the amount of calculation and emphasize the weight of the y-axis, i.e., the continuous coordinate, with a weight of 0 in the x-axis direction. In this transformation, When , the weight is 1. When the weight is Where b is the most persistent value of the persistent feature in all trials. When it is necessary to emphasize the influence of a feature with a smaller persistent coordinate, the weight of the feature with a smaller y should be increased. This example is used to select the weighting function for different features of interest when processing different data sets.

[0046] 3. Divide the grid on the coordinate axis, multiply the probability corresponding to each point by the weighted value, and then add the sum at this point to get the weighted sum of each point , these weighted sums together form a persistence surface.

[0047] Then the persistence surface corresponding to each pixel grid is integrated to obtain the pixel value of each pixel grid , and now the grid is drawn according to the pixel value. The weighted persistence table can be obtained as Figure 3 As shown. (a) is the original chart that only records the birth-death coordinates without processing, and (b) is the horizontal axis of birth time and the vertical axis of duration time, that is, the value obtained by subtracting birth from death. It is equivalent to making a linear transformation based on (a). (c) is the grid chart obtained by strengthening the continuous features of (b), which is more conducive to observing the duration of its continuous features, that is, the time span of the topological features from birth to death.

[0048] In the duration - birth time image (b), by calculating the mean and variance of the duration, the calculation results of the mean and variance of the topological feature duration of pore - fissure type, pore - cavity type, and inter - crystalline pore type rocks are shown in Table 1. The larger the mean, the longer the average lifespan of the topological feature, indicating that there are more pore structures that persist at a larger scale in the reservoir. These structures may be large pores or well - connected fractures. A smaller mean means that most of the topological feature durations are short, that is, the pore structure changes at a smaller scale, which usually indicates that the pore structure has a small size and a relatively uniform distribution. Therefore, the smaller the mean, the smaller the heterogeneity of the reservoir. The larger the variance, the more dispersed the duration distribution of the topological feature, indicating that there are significant differences in pore structures in the reservoir. Some topological features may have a very long lifespan, while others are very short, indicating that there are pore structures of different scales and connectivity in the reservoir, resulting in a higher degree of heterogeneity. So, the smaller the variance, the smaller the heterogeneity of the reservoir. According to the calculation results, the heterogeneity: pore - cavity type Pore - fissure type Inter - crystalline pore type.

[0049] Table 1 Mean and variance of topological feature durations of different rock samples During the processing of the persistence diagram, the key distance index H is extracted from the PD. This index is based on the "birth, b " and "death, d " scales of the PD points, and is determined by calculating the distances of the centroid P(xc, yc) relative to the diagonal and the death axis of the PD and . The calculation formula of the H index is:

[0050] where is the lifespan of the longest - lived point in the PD, used for normalization. The lower the value of the H index, the higher the heterogeneity of the rock pore structure, thus providing a new quantitative tool for predicting the physical properties of rocks. Among them, the persistence diagram (PD) of the aforementioned 3 samples is calculated by the above - mentioned method, and their quantitative index H is calculated respectively. The results are shown in Figure 4 , 5 , 6 respectively. Among them, Figure 4 , 5 , 6 are the calculation results of pore - fissure type, pore - cavity type, and inter - crystalline pore type rocks respectively. The figure includes the digital images and PD diagrams of each reservoir and the position of the centroid, Figure 5The H value of the shown pore reservoir is small, probably because the pore-type reservoir contains relatively large pores, which may be formed due to dissolution, biological activities or other geological processes. The sizes of the pores vary greatly, with different shapes and relatively discrete distributions. Such significant differences lead to high heterogeneity. It is also possible that the connectivity in the reservoir is poor, resulting in complex flow paths for fluids and large variations in permeability. This uneven connectivity also increases heterogeneity. And Figure 6 the H value of the shown intercrystalline pore reservoir is large, probably because its pores are mainly tiny pores existing between mineral crystals. These pores are usually small in size and evenly distributed, and the flow paths are relatively uniform. Although the number is small, the connectivity is usually good. The uniform spatial distribution makes the permeability relatively uniform, and thus the heterogeneity is weak. By comparing with the conclusion obtained from the mean variance of the duration-birth time diagram, the results can match well, further verifying the rationality of the proposed parameter and providing stronger support for heterogeneity analysis.

[0051] The innovation of this method lies in determining the centroid by weighted averaging of the probability density function (PDF) of the PD points , and a method for qualitatively analyzing the heterogeneity characteristics from the mean and variance information of the duration-birth time diagram is proposed. Finally, the relevant heterogeneity quantification index H is used to check the analysis results. Refer to (Jiang F, Tsuji T, Shirai T. Pore geometry characterization by persistent homology theory[J]. Water Resources Research, 2018, 54(6): 4150-4163). This index is based on two key distances and determined from the centroid position, where is the distance from the centroid to the PD diagonal, is the distance from the centroid along the diagonal direction to the death axis. and values respectively reflect the lifespan of the PD points and the emergence stage of the topological structure. A low value indicates high heterogeneity, while a low value indicates the rapid emergence of the topological structure, which is another sign of structural heterogeneity. The PD point with the longest lifespan is used to normalize H. The final result comparison shows the universality and comparability of the method for qualitatively analyzing heterogeneity results from the mean variance. This method improves the quantitative evaluation ability of the pore structure heterogeneity of geological reservoirs and provides assistance for the research and production in the field of karst reservoirs.

[0052] Although the content of the present invention has been described in detail through the above preferred embodiments, it should be recognized that the above description should not be considered as a limitation of the present invention. After those skilled in the art have read the above content, various modifications and alternatives to the present invention will be obvious. Therefore, the protection scope of the present invention should be defined by the appended claims.

Claims

1. A method for evaluating the geometric heterogeneity of a karst reservoir, characterized in that, Including: Performing micro-computed tomography on a karst reservoir sample to obtain a three-dimensional CT image of its internal pore structure; Performing binarization processing on the CT image, and using image segmentation technology to divide the pixel points in the image into a background representing pores and a foreground representing minerals; Based on the binarized processed image, applying a pore network extraction algorithm to extract the spatial distribution information of pore bodies from the binarized processed image, and constructing the largest sphere within the pore space, and the center point and radius information of the sphere constitute the sphere cloud data representing the pore bodies; Analyzing the extracted sphere cloud data using persistent homology theory analysis to calculate a persistence PD diagram; Calculating a heterogeneity quantification index H from the persistence diagram, and the lower the value of the index H, the higher the heterogeneity of the rock pore structure.

2. The evaluation method according to claim 1, characterized in that The karst reservoir sample includes pore-fracture type, pore-cavity type and intercrystalline pore type karst reservoirs.

3. The evaluation method according to claim 1, wherein For the binarization processing, by applying an adaptive threshold algorithm, the threshold is automatically determined according to the local statistical characteristics of the image to improve the discrimination accuracy and accurately distinguish the pore space and mineral matrix of the rock sample.

4. The evaluation method according to claim 1, characterized in that, The pore network extraction algorithm can be selected from the maximum ball algorithm.

5. The evaluation method according to claim 1, characterized in that, The specific persistent homology theory analysis is as follows: (1) Constructing a Rips complex by considering the distances between data points; (2) Capturing and recording the topological features of the data set, including the time when the topological feature starts to appear as the birth time and the time when it disappears as the death time, to obtain the persistence time of each topological feature; (3) Visualizing the topological features through the persistence PD diagram for representing the spatial distribution of pore bodies.

6. The evaluation method according to claim 5, wherein In the persistent homology theory analysis, the construction of the Rips complex considers the geometric distances between data points, uses the sphere radius as the filtration parameter ε, and its value range continuously increases from 0 to obtain an image of the topological model features from birth to extinction, ensuring the comprehensive capture of topological features.

7. The evaluation method according to claim 1, characterized in that The drawing of the persistence diagram is based on the core density prediction algorithm, and its density calculation formula is shown in Equation (1); Formula (1) Wherein: is the probability density value of the topological feature point; is the total number of sample data points; is a data point in the sample data with multiple dimensions, or a vector, where each dimension corresponds to the value of the data point on different features or attributes, and the coordinates in persistent homology are , where b is the birth time and d is the death time; is the Gaussian kernel function, indicating the kernel function related to the data point with a bandwidth of The expression of the Gaussian kernel function is: Formula (2) Among them, is a variable, representing the distance to the data point That is, ; is the bandwidth, which is used to control the width of the kernel function and determines the smoothness of the estimation.

8. The evaluation method according to claim 7, characterized in that, In the persistence diagram, the persistence time of each topological feature is calculated by subtracting its birth time from its death time, and the topological features with a persistence time greater than a preset threshold are identified as signals, and the rest are noise, which is due to the randomness and uncertainty in the data and may introduce false topological features to interfere with the true features; among them, data smoothing and noise processing methods are used to handle the noise.

9. The evaluation method according to claim 1, wherein The statistical parameters describing the topological feature distribution in the persistence PD diagram are the mean and variance of the persistence time, providing quantitative information for the heterogeneity of the reservoir pore structure.

10. The evaluation method according to claim 1, characterized in that The calculation formula of the heterogeneity quantification index H is shown in Equation (3): Formula (3) Among them, and are the distances from the centroid to the PD diagonal and the death axis, is the lifespan of the longest-lived point in PD, which is used for normalization to ensure the comparability of H values.

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