# Quantitative Characterization of Tight Rock Microstructure of Digital Core

Authors: Yuwei Liu; Shuping Wang; Rongchen Zheng; Haosen Li
Journal: Geofluids
 (2022)

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## Abstract

The fluid flow is closely related to the reservoir microstructure. And the pore throat is small, and the pore structure is complex of tight reservoirs, so the fluid flow mechanism is different from the conventional sandstones. In this paper, the sample size and scanning accuracy are determined by mercury-pressure experiments, and the gray-scale images of core samples are enhanced, filtered, and noise reduced, segmented by Avizo software, and finally 3D digital cores are constructed to realize quantitative characterization of pore throat parameters. The results show the following: (i) It is highly accurate to determine 3D digital core by comparing porosity measurement and calculating porosity; (ii) the average pore radius of the three samples is more than 7μm, the pore number is less than 651, the average throat length is greater than 159 μm, and the percentage of connected pore volume is above 95%; (iii) large pores are mainly developed in the reservoir, while a certain number of isolated pores exist, and the connected pores are distributed in sheets and strips; (iv) the pores of tight reservoir are mainly micron pores, and the distribution frequency histogram of pore radius is single peak; (v) porosity is related to connectivity, pore radius, and pore number; and (vi) the influence of throat on porosity and permeability is greater than that of pore. This paper is helpful for quantitative evaluation of reservoir microscopic parameters and provides technical support for visualization and quantitative characterization of rock microstructure.


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## Body

## 1. Introduction

Tight sandstone gas is an important field of increasing reserves and production in the world; it plays an important role in unconventional oil and gas development [1]. At present, most of the large tight sandstone gas reservoirs found in China belong to lithologic gas reservoirs, the accumulation of natural gas is mainly controlled by lithology, most of them are first densified and then formed, the characteristics of near-source accumulation are obvious, and it generally has the characteristics of hydrocarbon generation by wide covering and diffuse charging [2]. Influenced by sedimentation, diagenesis, and tectonism, the pore structure of tight sandstone reservoir is generally more complex and more heterogeneous, the pore throat can reach micro-nanoscale, the change of pore structure leads to the difference of gas migration and accumulation in tight sandstone reservoir, and the study of pore structure of this kind of reservoir must be the key [3]. The research on pore structure of tight sandstone can be divided into three categories in terms of experimental means [4]: (1) direct observation method, casting thin section, scanning electron microscopy, and other methods; (2) indirect measurement, mainly on the capillary pressure curve measurement; and (3) the numerical simulation method is mainly the 3D reconstruction of pore structure.The advantage of direct observation is that it can provide intuitive 2D image information of the pore-throat system; the pore-throat morphology was observed directly, through the processing and analysis of images, and obtained pore throat size and distribution information; the examples include casting thin sections and scanning electron microscopy [5]. Map Info software was used to extract the area, perimeter, center point coordinates of cavity and throat, throat diameter, pore coordination number, pore connectivity, and other information from the image of cast thin section [6]. SPSS software was used for statistical analysis of pore cavity and throat area, pore coordination number, and throat diameter, but due to the magnification limit, smaller nanoscale pore throats were not observed, scanning electron microscopy is an electronic optical instrument used to observe the surface structure of objects, and the pore shape and distribution of shale were described qualitatively by field emission scanning electron microscopy (FSEM) or combined with focused ion beam scanning electron microscopy (FSEM) and described the evolution of secondary organic matter pores in cores [7, 8].The indirect determination method can obtain the pore throat distribution information of core by mathematical conversion of test data, including gas adsorption synchrotron radiation small angle X-ray scattering technology core mercury injection analysis and nuclear magnetic resonance technology; however, the pore morphology cannot be directly displayed and observed. Gas adsorption method is divided into nitrogen and carbon dioxide gas adsorption test two methods; BET model is often used as the calculation method of specific surface measurement in nitrogen adsorption method; the measuring range is 1-200 nm [9]; however, it is generally considered that the nitrogen adsorption method is not accurate enough to measure pores above 100 nm. The carbon dioxide adsorption rule is obtained by using the D-R equation, pores larger than 0.35 nm can be measured [10], and the synchrotron radiation small angle X-ray scattering (SAXS) technique is used to study the internal structure characteristics of materials with non-uniform electron density at nanometer scale. The porosity and pore size distribution of coal were measured by SAXS technology, this method is much faster and cheaper, and there is no need to make other complicated samples [11]. Nuclear magnetic resonance (NMR) technology is another innovation in the study of reservoir microstructure, and it is closely related to the properties of fluid in the pores [12].Numerical simulation is the most effective method to obtain pore structure parameters; it can obtain the information of pore-throat shape, size, distribution, and pore-throat connectivity. Pang et al. [13] pointed out that 3D images allow one to map the internal connectivity of pores, grain structures, and primary/secondary pores. With the wide application of X-ray CT in rock physics experiment and the development of computer technology, the bridge between core microstructure and macroscopic physical properties is constructed. Digital core will play an important role in rock physics research and application as a research platform for microscopic seepage and conductivity characteristics [14].Due to the low accuracy of conventional CT scans, nanoscale pores in dense reservoirs cannot be accurately identified, resulting in low accuracy of the reconstructed model, and nano-CT makes up for this deficiency [15]. In this paper, a method of constructing 3D digital core by combining CT scanning with mercury intrusion analysis is proposed, core size and CT scan resolution were determined by mercury injection method, nano-CT scan and subsequent image processing were performed, high precision digital core construction. The digital cores obtained by this method are closer to the experimental results in porosity and permeability.


## 2. Core Micron CT Scan

The cores used in this study are real cores, provided by key Laboratory for Marine Oil and Gas Exploitation, Sinopec. The three core samples in this study were taken from Shan1, Shan2, and He3 in the Hangjinqi area. The lithological characteristics of these three reservoirs are shown in Table1.Table 1
Lithological characteristics.
ReservoirLithological characteristicsQuartz content (%)Shan 1Lithic quartz (pebbly) coarse sandstone81.6Shan 2Lithic (pebbly) coarse sandstone65.6He 3Lithic quartz (pebbly) coarse sandstone71.8These three reservoirs of fillings are mainly kaolinite and chlorite with small amounts of calcite, dolomite, pyrite, etc. The sandstone sorting is predominantly medium-good. The rounding is predominantly sub-angular, followed by sub-rounded. The overall structural maturity is low. The characteristics of porosity and permeability are shown in Table2.Table 2
Porosity and permeability characteristics.
ReservoirPorosity (%)Average porosity (%)Permeability (mD)Average permeability (mD)Shan 10.6-23.99.070.009-90.94.274Shan 20.1-19.180.008-5.880.705He 30.4-23.210.670.024-59.42.19From the porosity and permeability relationship curves (Figure1), it can be seen that Shan1 is a high permeability reservoir and Shan2 and He3 are low pore extra low permeability or low pore ultra-low permeability reservoirs.Figure 1
Porosity-permeability relationship.
(a)
Shan1 member(b)
Shan2 member(c)
He 3 memberThe reconstruction of cores is based on CT scanning, which has the advantages of nondestructive sample and easy operation compared with sequence imaging, focused scanning, and scanning electron microscope (SEM) methods [16]. Three core samples were scanned and tested with the GE Phoenix Nanotom S-type nano-CT scanner (Figure 2). X-CT scanning is to penetrate X-rays into the core sample, rotate the sample 360° (Figure 3), obtain a large number of X-ray projection images, and use these images to reconstruct a 3D core model.Figure 2
Phoenix Nanotom S CT scanner.Figure 3
X-ray CT scan image layout.Since X-rays produce energy attenuation in contact with the core as they pass through the core, the absorption coefficient (i.e., attenuation coefficient) of the core is related to the internal structure and density of the core. Therefore, the pore structure and relative density inside the core can be determined by the energy attenuation of X-rays when penetrating the core sample as reflected by CT images [17]. Since the CT scans have a resolution limit, when the pore throat size is smaller than the CT scan resolution, it will not be identified, so the digital core will not contain micropores below the scan resolution.


## 3. CT Image Processing

### 3.1. Core Size Determination

Three samples were selected in this study, and the porosity and permeability are shown in Table3.Table 3
Basic sample parameter table.
Sample numberPorosity (%)Permeability (mD)1111.63650.02613411.98680.2945518.0950.1129The permeability and porosity of these three cores are positive correlation but poor correlation between porosity and permeability of sample 11 (Figure4). So the analysis of the parameters affecting porosity can indirectly analyze its effect on permeability.Figure 4
Permeability and porosity curve.Since CT scans have a resolution limit, when the pore throat size is smaller than the CT scan resolution, it will not be identified, so the digital core will not contain micropores below the scan resolution [18]. If there are a large number of pores in the core that are lower than the resolution of CT scan, it will lead to a large error between the porosity of the digital core and the experimental porosity, making the results inaccurate. Therefore, in order to eliminate the error between porosity and CT scan resolution, this paper combines the results of core mercury penetration experiment to determine the distribution range of core porosity and then determine the CT scan resolution. From the results of the block sample mercury penetration experiment (Figure 5), it can be seen that the pore radius of the studied reservoir is distributed between 0.0046 μm and 0.5611 μm, and the scanning resolution of the cores is shown in Table 4.Figure 5
The mercury penetration experiment curve.Table 4
Sample resolution.
Sample numberScanning resolution (μm)111.5341.97511.9


### 3.2. Image Enhancement

Because of the instrument parameter settings during the scanning process, the overall brightness of the CT 2D slice image is dark, showing that the contrast of pores, matrix, and minerals is not high, so the image enhancement process is needed. The image enhancement processing method used in this study is histogram grayscale transformation, which converts the input grayscale values with smaller grayscale values in CT 2D slices to the output grayscale values with larger grayscale values, improves the contrast of CT images, increases the grayscale difference between pores and matrix in CT images, and facilitates the segmentation of 3D digital cores and other related processing, where the dark black area represents the pore space and the gray and white areas represent the matrix (Figure6).Figure 6
Image enhancement diagram.


### 3.3. Image Filtering and Noise Reduction

In the process of CT scanning, the images will have noise problems due to the environment and the equipment itself, so the images need to be processed for noise reduction while preserving as much image features and key information as possible [19].Median filtering is a typical method in nonlinear filtering; it is one of the most commonly used image preprocessing techniques. Median filtering preserves the details of the image well. In the process of noise reduction, the boundary does not blur [20]. Linear filtering cannot do that. Median filtering does not generate new pixel values and is not affected by singular values.In AVIZO software, median filtering uses morphological operators to set the pixel values of defined neighborhoods as median values. When the data volume contains non-Gaussian noise or very small artifacts, the median filter can get good results. So we use median filtering algorithm in image filtering and noise reduction. The image filtering and noise reduction process of the 3 cores is shown in Figure7.Figure 7
Intercept position and filtering noise reduction.
(a)
Sample 51(b)
Sample 11(c)
Sample 34


### 3.4. Picture Segmentation

In order to separate the pores and fractures from the skeleton in CT images and facilitate the creation of digital core models, the images need to be segmented [21]. Threshold segmentation method is the most commonly used method in image segmentation processing, which is easy to operate, simple in principle, stable in performance, and efficient in operation and can simplify the analysis process and greatly compress the amount of data [22]. So this method is chosen to segment the image (Figure 8).Figure 8
Binary segmentation and pore filling.
(a)
Sample of 51(b)
Sample of 11(c)
Sample of 34


## 3.1. Core Size Determination

Three samples were selected in this study, and the porosity and permeability are shown in Table3.Table 3
Basic sample parameter table.
Sample numberPorosity (%)Permeability (mD)1111.63650.02613411.98680.2945518.0950.1129The permeability and porosity of these three cores are positive correlation but poor correlation between porosity and permeability of sample 11 (Figure4). So the analysis of the parameters affecting porosity can indirectly analyze its effect on permeability.Figure 4
Permeability and porosity curve.Since CT scans have a resolution limit, when the pore throat size is smaller than the CT scan resolution, it will not be identified, so the digital core will not contain micropores below the scan resolution [18]. If there are a large number of pores in the core that are lower than the resolution of CT scan, it will lead to a large error between the porosity of the digital core and the experimental porosity, making the results inaccurate. Therefore, in order to eliminate the error between porosity and CT scan resolution, this paper combines the results of core mercury penetration experiment to determine the distribution range of core porosity and then determine the CT scan resolution. From the results of the block sample mercury penetration experiment (Figure 5), it can be seen that the pore radius of the studied reservoir is distributed between 0.0046 μm and 0.5611 μm, and the scanning resolution of the cores is shown in Table 4.Figure 5
The mercury penetration experiment curve.Table 4
Sample resolution.
Sample numberScanning resolution (μm)111.5341.97511.9


## 3.2. Image Enhancement

Because of the instrument parameter settings during the scanning process, the overall brightness of the CT 2D slice image is dark, showing that the contrast of pores, matrix, and minerals is not high, so the image enhancement process is needed. The image enhancement processing method used in this study is histogram grayscale transformation, which converts the input grayscale values with smaller grayscale values in CT 2D slices to the output grayscale values with larger grayscale values, improves the contrast of CT images, increases the grayscale difference between pores and matrix in CT images, and facilitates the segmentation of 3D digital cores and other related processing, where the dark black area represents the pore space and the gray and white areas represent the matrix (Figure6).Figure 6
Image enhancement diagram.


## 3.3. Image Filtering and Noise Reduction

In the process of CT scanning, the images will have noise problems due to the environment and the equipment itself, so the images need to be processed for noise reduction while preserving as much image features and key information as possible [19].Median filtering is a typical method in nonlinear filtering; it is one of the most commonly used image preprocessing techniques. Median filtering preserves the details of the image well. In the process of noise reduction, the boundary does not blur [20]. Linear filtering cannot do that. Median filtering does not generate new pixel values and is not affected by singular values.In AVIZO software, median filtering uses morphological operators to set the pixel values of defined neighborhoods as median values. When the data volume contains non-Gaussian noise or very small artifacts, the median filter can get good results. So we use median filtering algorithm in image filtering and noise reduction. The image filtering and noise reduction process of the 3 cores is shown in Figure7.Figure 7
Intercept position and filtering noise reduction.
(a)
Sample 51(b)
Sample 11(c)
Sample 34


## 3.4. Picture Segmentation

In order to separate the pores and fractures from the skeleton in CT images and facilitate the creation of digital core models, the images need to be segmented [21]. Threshold segmentation method is the most commonly used method in image segmentation processing, which is easy to operate, simple in principle, stable in performance, and efficient in operation and can simplify the analysis process and greatly compress the amount of data [22]. So this method is chosen to segment the image (Figure 8).Figure 8
Binary segmentation and pore filling.
(a)
Sample of 51(b)
Sample of 11(c)
Sample of 34


## 4. Analysis of Rock Microstructure

### 4.1. Pore Space 3D Visualization Characterization

3D digital core can directly and truly reflect the microscopic pore space inside the core sample and can be used to study the distribution characteristics of pore inside the rock. 3D visualization of digital core is on the basis of image binarization segmentation, adjusts the transparency of rock skeleton or pore and then gets the internal different rock composition distribution characteristics of the 3D space. In this paper, GE Phoenix Datosx 2 Acq X software is used to reconstruct the digital 3D model of the scanned data, from the image data to extract the centerline of the interconnected pores, the binary image, and the gray image processing. Firstly, it calculates the distance map segmentation image and then the binary image thinning, and a series of interconnected voxel pore is obtained. Voxel pore is converted into a spatial graphic object. The spatial graphic is composed of nodes and segments, where nodes are branch points and endpoints, representing the pore space of the core, and segments are curves connecting nodes, representing the throat space of the core. Figure9 is 3D pore space models of three cores.Figure 9
Pore-throat model.
(a)
Sample 51(b)
Sample 11(c)
Sample 34The digital core porosity results in Table5 show that based on the experimental results, the maximum error between digital core porosity and experimental porosity is 0.49%. Because the error is very small, so the result of digital core reconstruction is accurate (Figure 10).Table 5
Comparison between digital core porosity and experimental porosity.
Sample numberExperimental porosity (%)Digital core porosity (%)Error (%)1111.636511.6640.23633411.986811.9910.035518.0958.0550.4941Figure 10
Experimental pore and digital pore comparison.


### 4.2. Pore Space Connectivity Visualization Characterization

Based on the 3D core pore throat distribution model, the 3D core connectivity is analyzed. In this study, we use the seed filling method to analyze the connectivity of pores. The connectivity between each pore pixel and other pore pixels is detected, and the mutually connected pore pixels are marked as a connectivity domain [23]. This filling method has three choices of connectivity states in 3D conditions, which are 6 adjacent, 18 adjacent, and 26 adjacent. The more adjacent numbers, the more memory is needed and the longer operation time required in processing [24]. For this reason, we process by selecting 18 adjacent. The connectivity model of three cores is shown in Figure 11. The colors in the figure represent different connectivity domains, and 8 colors are selected to mark different connectivity domains cyclically, independent of the area of the connected part.Figure 11
Connectivity model.
(a)
Sample 51(b)
Sample 11(c)
Sample 34In this study, pores are classified into three categories: major pores, minor pores, and dead pores. Pores that penetrate the model are major pores, and such pores contribute greatly to the permeability in a particular direction. Secondary pores are located on the model boundary, but have an impact on pore connectivity and still contribute to permeability in specific directions. The dead pores are located inside the model and do not contribute to the permeability. This classification of pores is more conducive to the visual characterization of pore connectivity and provides a basis for quantitative evaluation of pore connectivity.From the table of connected pore volume percentage (Table6), it can be seen that the connected pore volume percentage is proportional to the porosity (Figure 12), but there is no significant relationship with the permeability. It can be seen that the permeability of tight reservoirs is not directly related to the percentage of connected pore volume.Table 6
Connected pore volume.
Sample numberConnected pore volume (%)1196.5173498.8635195.426Figure 12
Connectivity pore volume relationship with porosity and permeability.
(a)
Connected pore volume relationship with porosity(b)
Connected pore volume relationship with permeability


### 4.3. Pore Network Modeling

The 3D pore network model is to find out the relationship between the location of pores and howlers in the core. At present, there are four main methods to build 3D pore network models: multidirectional scanning method, pore space median method, maximum sphere algorithm, and Voronoi polyhedral method. The maximum sphere method is simple, and the constructed model is stable. This method can quickly reconstruct the pore-throat network and can accurately preserve the pore-throat distribution characteristics and connectivity characteristics [25]. In this paper, we choose the maximum sphere method to construct the 3D pore throat model.The maximum sphere method is to select any point in the pore pixels and extend it as the center of the sphere in all directions until the boundary of the sphere touches the nearest skeleton pixel, and the set of all pixels in the formed area is called the maximum sphere, and finally a series of spheres of different sizes fill the pore of the 3D core [26]. In the 3D pore network model, the pore and throat are represented by a sphere and a cylinder, respectively. Each core contains a certain number of isolated pores, most of these pores are small in size and scattered, and only sample 51 has larger isolated pores present (Figure 13).Figure 13
Ball and stick models.
(a)
Sample 51(b)
Sample 11(c)
Sample 34The digital core pore space processed by the maximal ball algorithm can be divided into pore part and throat part. For the extracted 3D pore network model, count the pore network size distribution and analyze the connectivity characteristics of pore network. Through the statistical analysis of pore radius, throat radius, and throat length of pore network model, the quantitative characterization of rock micropore structure can be realized.


### 4.4. Analysis of Pore and Throat Parameters

The pore and throat are important parts of the core, where the pore is the storage of fluid and the throat is the channel of fluid transport. The fluid flow is in different pores and throats in the rock. For the simplified pore-throat network structure model, statistics on parameters such as number and size of pores and throats and the pore throat structure characteristics of real cores can be understood.


#### 4.4.1. Pore Parameters

Pore space is the main storage space of fluid in the core, and its space size is directly related to the sphere of “ball and stick model.” The sphere radius represents the pore volume, and the sphere distribution density represents the number of pores, so the sphere characteristics in the pore throat model can represent the pore characteristics.1. The Pore Numbers. The pore number and calculated porosity of the three cores were counted, and the specific data are shown in Table 7.Table 7
Statistical table of pore number.
Sample numberThe number of pores112313465151120From the results (Figure14), it can be seen that the number of pores is positively correlated with the porosity. The number of pores of sample 11 was 111 more than that of sample 51, and the porosity of sample 11 was 3.609% larger than that of sample 51. The number of pores of sample 34 was 420 more than the number of pores of sample 11, and the porosity of sample 34 was 0.327% greater than the porosity of sample 11. The number of pores is positively correlated with the porosity and permeability, but the number of pores is not the main factor affecting the porosity and permeability.Figure 14
Pore number relationship with porosity and permeability.
(a)
Pore number relationship with porosity(b)
Pore number relationship with permeability2. The Pore Radius. Core pore radius of pore volume is very important to the size of the decisive role, so the distribution of pore radius must have a detailed understanding of the situation. The equivalent pore radius obtained here is the maximum inscribed circle radius, which is very close to the actual value and can basically replace the real value. The average pore radius and pore volume of three cores are counted, and the specific data are shown in the table.Figure15 and Table 8 show the statistics of pore radius. The pore radius distribution curves of all three samples show a typical unimodal distribution. The highest point of the curve corresponds to the smallest pore radius, and the curve decreases rapidly, which indicates that the core has more small pore structures. The heterogeneous distribution of equivalent pore diameters also indicates the complex pore structure and poor homogeneity. The major pore radii of the three samples were as follows: 1.22-67.88 μm; 1.18-16.3 μm; and 0.93-42.14 μm. Sample 34 homogeneity is the best.Figure 15
Pore radius distribution curve.
(a)
Sample 11(b)
Sample 34(c)
Sample 51Table 8
Pore radius.
Sample numberPore radius (μm)Pore radius peak (μm)Pore radius peak percentageThe average pore radius (μm)111.22-149.012.388.23%22.95341.18-139.031.1835.33%6.99510.93-137.40.9325%1.53Sample 11 had the largest major pore radius and average pore radius, but the porosity and permeability were not the largest in the three samples, indicating that the porosity size was not only related to the average pore radius (Figure16).Figure 16
Average pore radius relationship with porosity and permeability.
(a)
Average pore radius relationship with porosity(b)
Average pore radius relationship with permeability3. The Pore Volume. Table 9 and Figure 17 show that the porosity and permeability of sample 34 are the largest in the three samples, but the pore volume size is not the largest. The comprehensive analysis shows that the size of porosity needs to consider the influence of pore number, average pore radius, and pore volume.Table 9
Pore volume.
Sample numberThe pore volume (×107 μm3)1187546714.5533454026628.255126689466.388Figure 17
Pore volume relationship with porosity and permeability.
(a)
Pore volume relationship with porosity(b)
Pore volume relationship with permeability


#### 4.4.2. Throat Parameters

The throat is the channel for fluid flow in the core. The permeability of the core is related to the radius and length of the throat channel. The pore throat model obtained by the maximum ball method; the “stick” is the throat. The radius and length of the throat can be analyzed according to the pore throat model.1. The Throat Radius. Figure 18 and Table 10 show the statistics of throat radius. The curve is widely distributed. Except for the more occupied throats, the curve decreases slowly, indicating that there are more throats with larger sizes in the core, which is conducive to fluid flow.Figure 18
Histogram of throat radius.
(a)
Sample 11(b)
Sample 34(c)
Sample 51Table 10
Throat radius.
Sample numberThroat radius (μm)Throat radius peak (μm)Throat radius peak percentageThe average radius length (μm)111.31-91.75.91/6.27/7.334.71%22.48341.99-105.671.99/7.284.84%31.99511.2-63.67.8/13.92/21.025.88%18.91From the results (Figure19), it is seen that the average radius of the throat is well correlated with the porosity and permeability.Figure 19
Average throat radius relationship with porosity and permeability.
(a)
Average throat radius relationship with porosity(b)
Average throat radius relationship with permeability2. The Throat Length. For the average length of the throat (Table 11 and Figure 20), both are proportional to the porosity and permeability. Since the longer the length, the more pores connected by the throat, the better connectivity of the pore and throat and, thus, the greater the permeability [27]. Through the quantitative study of pore parameters and throat parameters, it can be found that the influence of throat on porosity and permeability is greater than that of pore.Table 11
Throat length.
Sample numberThe average throat length (μm)11181.01334182.16251159.436Figure 20
Average throat length relationship with porosity and permeability.
(a)
Average throat length relationship with porosity(b)
Average throat length relationship with permeability


## 4.1. Pore Space 3D Visualization Characterization

3D digital core can directly and truly reflect the microscopic pore space inside the core sample and can be used to study the distribution characteristics of pore inside the rock. 3D visualization of digital core is on the basis of image binarization segmentation, adjusts the transparency of rock skeleton or pore and then gets the internal different rock composition distribution characteristics of the 3D space. In this paper, GE Phoenix Datosx 2 Acq X software is used to reconstruct the digital 3D model of the scanned data, from the image data to extract the centerline of the interconnected pores, the binary image, and the gray image processing. Firstly, it calculates the distance map segmentation image and then the binary image thinning, and a series of interconnected voxel pore is obtained. Voxel pore is converted into a spatial graphic object. The spatial graphic is composed of nodes and segments, where nodes are branch points and endpoints, representing the pore space of the core, and segments are curves connecting nodes, representing the throat space of the core. Figure9 is 3D pore space models of three cores.Figure 9
Pore-throat model.
(a)
Sample 51(b)
Sample 11(c)
Sample 34The digital core porosity results in Table5 show that based on the experimental results, the maximum error between digital core porosity and experimental porosity is 0.49%. Because the error is very small, so the result of digital core reconstruction is accurate (Figure 10).Table 5
Comparison between digital core porosity and experimental porosity.
Sample numberExperimental porosity (%)Digital core porosity (%)Error (%)1111.636511.6640.23633411.986811.9910.035518.0958.0550.4941Figure 10
Experimental pore and digital pore comparison.


## 4.2. Pore Space Connectivity Visualization Characterization

Based on the 3D core pore throat distribution model, the 3D core connectivity is analyzed. In this study, we use the seed filling method to analyze the connectivity of pores. The connectivity between each pore pixel and other pore pixels is detected, and the mutually connected pore pixels are marked as a connectivity domain [23]. This filling method has three choices of connectivity states in 3D conditions, which are 6 adjacent, 18 adjacent, and 26 adjacent. The more adjacent numbers, the more memory is needed and the longer operation time required in processing [24]. For this reason, we process by selecting 18 adjacent. The connectivity model of three cores is shown in Figure 11. The colors in the figure represent different connectivity domains, and 8 colors are selected to mark different connectivity domains cyclically, independent of the area of the connected part.Figure 11
Connectivity model.
(a)
Sample 51(b)
Sample 11(c)
Sample 34In this study, pores are classified into three categories: major pores, minor pores, and dead pores. Pores that penetrate the model are major pores, and such pores contribute greatly to the permeability in a particular direction. Secondary pores are located on the model boundary, but have an impact on pore connectivity and still contribute to permeability in specific directions. The dead pores are located inside the model and do not contribute to the permeability. This classification of pores is more conducive to the visual characterization of pore connectivity and provides a basis for quantitative evaluation of pore connectivity.From the table of connected pore volume percentage (Table6), it can be seen that the connected pore volume percentage is proportional to the porosity (Figure 12), but there is no significant relationship with the permeability. It can be seen that the permeability of tight reservoirs is not directly related to the percentage of connected pore volume.Table 6
Connected pore volume.
Sample numberConnected pore volume (%)1196.5173498.8635195.426Figure 12
Connectivity pore volume relationship with porosity and permeability.
(a)
Connected pore volume relationship with porosity(b)
Connected pore volume relationship with permeability


## 4.3. Pore Network Modeling

The 3D pore network model is to find out the relationship between the location of pores and howlers in the core. At present, there are four main methods to build 3D pore network models: multidirectional scanning method, pore space median method, maximum sphere algorithm, and Voronoi polyhedral method. The maximum sphere method is simple, and the constructed model is stable. This method can quickly reconstruct the pore-throat network and can accurately preserve the pore-throat distribution characteristics and connectivity characteristics [25]. In this paper, we choose the maximum sphere method to construct the 3D pore throat model.The maximum sphere method is to select any point in the pore pixels and extend it as the center of the sphere in all directions until the boundary of the sphere touches the nearest skeleton pixel, and the set of all pixels in the formed area is called the maximum sphere, and finally a series of spheres of different sizes fill the pore of the 3D core [26]. In the 3D pore network model, the pore and throat are represented by a sphere and a cylinder, respectively. Each core contains a certain number of isolated pores, most of these pores are small in size and scattered, and only sample 51 has larger isolated pores present (Figure 13).Figure 13
Ball and stick models.
(a)
Sample 51(b)
Sample 11(c)
Sample 34The digital core pore space processed by the maximal ball algorithm can be divided into pore part and throat part. For the extracted 3D pore network model, count the pore network size distribution and analyze the connectivity characteristics of pore network. Through the statistical analysis of pore radius, throat radius, and throat length of pore network model, the quantitative characterization of rock micropore structure can be realized.


## 4.4. Analysis of Pore and Throat Parameters

The pore and throat are important parts of the core, where the pore is the storage of fluid and the throat is the channel of fluid transport. The fluid flow is in different pores and throats in the rock. For the simplified pore-throat network structure model, statistics on parameters such as number and size of pores and throats and the pore throat structure characteristics of real cores can be understood.


### 4.4.1. Pore Parameters

Pore space is the main storage space of fluid in the core, and its space size is directly related to the sphere of “ball and stick model.” The sphere radius represents the pore volume, and the sphere distribution density represents the number of pores, so the sphere characteristics in the pore throat model can represent the pore characteristics.1. The Pore Numbers. The pore number and calculated porosity of the three cores were counted, and the specific data are shown in Table 7.Table 7
Statistical table of pore number.
Sample numberThe number of pores112313465151120From the results (Figure14), it can be seen that the number of pores is positively correlated with the porosity. The number of pores of sample 11 was 111 more than that of sample 51, and the porosity of sample 11 was 3.609% larger than that of sample 51. The number of pores of sample 34 was 420 more than the number of pores of sample 11, and the porosity of sample 34 was 0.327% greater than the porosity of sample 11. The number of pores is positively correlated with the porosity and permeability, but the number of pores is not the main factor affecting the porosity and permeability.Figure 14
Pore number relationship with porosity and permeability.
(a)
Pore number relationship with porosity(b)
Pore number relationship with permeability2. The Pore Radius. Core pore radius of pore volume is very important to the size of the decisive role, so the distribution of pore radius must have a detailed understanding of the situation. The equivalent pore radius obtained here is the maximum inscribed circle radius, which is very close to the actual value and can basically replace the real value. The average pore radius and pore volume of three cores are counted, and the specific data are shown in the table.Figure15 and Table 8 show the statistics of pore radius. The pore radius distribution curves of all three samples show a typical unimodal distribution. The highest point of the curve corresponds to the smallest pore radius, and the curve decreases rapidly, which indicates that the core has more small pore structures. The heterogeneous distribution of equivalent pore diameters also indicates the complex pore structure and poor homogeneity. The major pore radii of the three samples were as follows: 1.22-67.88 μm; 1.18-16.3 μm; and 0.93-42.14 μm. Sample 34 homogeneity is the best.Figure 15
Pore radius distribution curve.
(a)
Sample 11(b)
Sample 34(c)
Sample 51Table 8
Pore radius.
Sample numberPore radius (μm)Pore radius peak (μm)Pore radius peak percentageThe average pore radius (μm)111.22-149.012.388.23%22.95341.18-139.031.1835.33%6.99510.93-137.40.9325%1.53Sample 11 had the largest major pore radius and average pore radius, but the porosity and permeability were not the largest in the three samples, indicating that the porosity size was not only related to the average pore radius (Figure16).Figure 16
Average pore radius relationship with porosity and permeability.
(a)
Average pore radius relationship with porosity(b)
Average pore radius relationship with permeability3. The Pore Volume. Table 9 and Figure 17 show that the porosity and permeability of sample 34 are the largest in the three samples, but the pore volume size is not the largest. The comprehensive analysis shows that the size of porosity needs to consider the influence of pore number, average pore radius, and pore volume.Table 9
Pore volume.
Sample numberThe pore volume (×107 μm3)1187546714.5533454026628.255126689466.388Figure 17
Pore volume relationship with porosity and permeability.
(a)
Pore volume relationship with porosity(b)
Pore volume relationship with permeability


### 4.4.2. Throat Parameters

The throat is the channel for fluid flow in the core. The permeability of the core is related to the radius and length of the throat channel. The pore throat model obtained by the maximum ball method; the “stick” is the throat. The radius and length of the throat can be analyzed according to the pore throat model.1. The Throat Radius. Figure 18 and Table 10 show the statistics of throat radius. The curve is widely distributed. Except for the more occupied throats, the curve decreases slowly, indicating that there are more throats with larger sizes in the core, which is conducive to fluid flow.Figure 18
Histogram of throat radius.
(a)
Sample 11(b)
Sample 34(c)
Sample 51Table 10
Throat radius.
Sample numberThroat radius (μm)Throat radius peak (μm)Throat radius peak percentageThe average radius length (μm)111.31-91.75.91/6.27/7.334.71%22.48341.99-105.671.99/7.284.84%31.99511.2-63.67.8/13.92/21.025.88%18.91From the results (Figure19), it is seen that the average radius of the throat is well correlated with the porosity and permeability.Figure 19
Average throat radius relationship with porosity and permeability.
(a)
Average throat radius relationship with porosity(b)
Average throat radius relationship with permeability2. The Throat Length. For the average length of the throat (Table 11 and Figure 20), both are proportional to the porosity and permeability. Since the longer the length, the more pores connected by the throat, the better connectivity of the pore and throat and, thus, the greater the permeability [27]. Through the quantitative study of pore parameters and throat parameters, it can be found that the influence of throat on porosity and permeability is greater than that of pore.Table 11
Throat length.
Sample numberThe average throat length (μm)11181.01334182.16251159.436Figure 20
Average throat length relationship with porosity and permeability.
(a)
Average throat length relationship with porosity(b)
Average throat length relationship with permeability


## 4.4.1. Pore Parameters

Pore space is the main storage space of fluid in the core, and its space size is directly related to the sphere of “ball and stick model.” The sphere radius represents the pore volume, and the sphere distribution density represents the number of pores, so the sphere characteristics in the pore throat model can represent the pore characteristics.1. The Pore Numbers. The pore number and calculated porosity of the three cores were counted, and the specific data are shown in Table 7.Table 7
Statistical table of pore number.
Sample numberThe number of pores112313465151120From the results (Figure14), it can be seen that the number of pores is positively correlated with the porosity. The number of pores of sample 11 was 111 more than that of sample 51, and the porosity of sample 11 was 3.609% larger than that of sample 51. The number of pores of sample 34 was 420 more than the number of pores of sample 11, and the porosity of sample 34 was 0.327% greater than the porosity of sample 11. The number of pores is positively correlated with the porosity and permeability, but the number of pores is not the main factor affecting the porosity and permeability.Figure 14
Pore number relationship with porosity and permeability.
(a)
Pore number relationship with porosity(b)
Pore number relationship with permeability2. The Pore Radius. Core pore radius of pore volume is very important to the size of the decisive role, so the distribution of pore radius must have a detailed understanding of the situation. The equivalent pore radius obtained here is the maximum inscribed circle radius, which is very close to the actual value and can basically replace the real value. The average pore radius and pore volume of three cores are counted, and the specific data are shown in the table.Figure15 and Table 8 show the statistics of pore radius. The pore radius distribution curves of all three samples show a typical unimodal distribution. The highest point of the curve corresponds to the smallest pore radius, and the curve decreases rapidly, which indicates that the core has more small pore structures. The heterogeneous distribution of equivalent pore diameters also indicates the complex pore structure and poor homogeneity. The major pore radii of the three samples were as follows: 1.22-67.88 μm; 1.18-16.3 μm; and 0.93-42.14 μm. Sample 34 homogeneity is the best.Figure 15
Pore radius distribution curve.
(a)
Sample 11(b)
Sample 34(c)
Sample 51Table 8
Pore radius.
Sample numberPore radius (μm)Pore radius peak (μm)Pore radius peak percentageThe average pore radius (μm)111.22-149.012.388.23%22.95341.18-139.031.1835.33%6.99510.93-137.40.9325%1.53Sample 11 had the largest major pore radius and average pore radius, but the porosity and permeability were not the largest in the three samples, indicating that the porosity size was not only related to the average pore radius (Figure16).Figure 16
Average pore radius relationship with porosity and permeability.
(a)
Average pore radius relationship with porosity(b)
Average pore radius relationship with permeability3. The Pore Volume. Table 9 and Figure 17 show that the porosity and permeability of sample 34 are the largest in the three samples, but the pore volume size is not the largest. The comprehensive analysis shows that the size of porosity needs to consider the influence of pore number, average pore radius, and pore volume.Table 9
Pore volume.
Sample numberThe pore volume (×107 μm3)1187546714.5533454026628.255126689466.388Figure 17
Pore volume relationship with porosity and permeability.
(a)
Pore volume relationship with porosity(b)
Pore volume relationship with permeability


## 4.4.2. Throat Parameters

The throat is the channel for fluid flow in the core. The permeability of the core is related to the radius and length of the throat channel. The pore throat model obtained by the maximum ball method; the “stick” is the throat. The radius and length of the throat can be analyzed according to the pore throat model.1. The Throat Radius. Figure 18 and Table 10 show the statistics of throat radius. The curve is widely distributed. Except for the more occupied throats, the curve decreases slowly, indicating that there are more throats with larger sizes in the core, which is conducive to fluid flow.Figure 18
Histogram of throat radius.
(a)
Sample 11(b)
Sample 34(c)
Sample 51Table 10
Throat radius.
Sample numberThroat radius (μm)Throat radius peak (μm)Throat radius peak percentageThe average radius length (μm)111.31-91.75.91/6.27/7.334.71%22.48341.99-105.671.99/7.284.84%31.99511.2-63.67.8/13.92/21.025.88%18.91From the results (Figure19), it is seen that the average radius of the throat is well correlated with the porosity and permeability.Figure 19
Average throat radius relationship with porosity and permeability.
(a)
Average throat radius relationship with porosity(b)
Average throat radius relationship with permeability2. The Throat Length. For the average length of the throat (Table 11 and Figure 20), both are proportional to the porosity and permeability. Since the longer the length, the more pores connected by the throat, the better connectivity of the pore and throat and, thus, the greater the permeability [27]. Through the quantitative study of pore parameters and throat parameters, it can be found that the influence of throat on porosity and permeability is greater than that of pore.Table 11
Throat length.
Sample numberThe average throat length (μm)11181.01334182.16251159.436Figure 20
Average throat length relationship with porosity and permeability.
(a)
Average throat length relationship with porosity(b)
Average throat length relationship with permeability


## 5. Conclusion

(1)
Digital core technology can be an effective supplement to conventional rock physics experiments and theoretical methods. The core slices obtained after CT scanning are digitized, and the two-dimensional graphics are transformed into 3D images to quantitatively characterize the pore characteristics and pore-throat characteristics of core samples so that the subsequent research can be more targeted. Although the digital core makes up for the deficiency of conventional rock physics experiments, but the computer memory in the calculation process needs to be 3-4 times that of CT scan data, which makes the data processing of big data subject to certain limitations(2)
It can be observed through the pore-throat model constructed, large pores are mainly developed in the reservoir, while a certain number of isolated pores exist; it can intuitively reflect the complex and changeable characteristics of tight reservoir pore structure. From the connectivity model, connected pores are distributed in sheets and strips, the percentage of connected pore volume is proportional to porosity, the connected pore volume percentage of the three samples is all higher than 95%, and the porosity is still less than 12%, indicating that porosity is related not only to connectivity but also to pore radius and pore number(3)
From the statistical results of porosity and throat radius, the pores of tight reservoir are mainly micron pores, and the distribution frequency histogram of pore radius is single peak. Through the quantitative study of pore parameters and throat parameters, it can be found that the influence of throat on porosity and permeability is greater than that of pore. The reasons of poor porosity and low permeability in tight reservoirs are as follows: (i) small pore size; (ii) the distribution range of pore radius is small; (iii) the proportion of main pore radius to all pore radius is small; (iv) the number of pores is small; and (v) the throat radius has a wide distribution range, but the size is small, and the distribution frequency of the main throat radius accounts for a small proportion of the total roar radius



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