Pore Structure Quantitative Characterization of Tight Sandstones Based on Deep Learning and Fractal Analysis

Abstract

Sandstone reservoirs exhibit strong heterogeneity and complex microscopic pore structures, presenting challenges for quantitative characterization. This study investigates the Chang 8 tight sandstone reservoir in the Jiyuan, Ordos Basin through analyses of its physical properties, high-pressure mercury injection (HPMI), casting thin sections (CTS), and scanning electron microscopy (SEM). Deep learning techniques were employed to extract the geometric parameters of the pores from the SEM images. Fractal geometry was applied for the combined quantitative characterization of pore parameters and fractal dimensions of the tight sandstone. This study also analyzed the correlations between the fractal dimensions, sample properties, pore structure, geometric parameters, and mineral content. The results indicate that the HPMI-derived fractal dimension (D_MIP) reflects pore connectivity and permeability. D_MIP gradually increases from Type I to Type III reservoirs, indicating deteriorating pore connectivity and increasing reservoir heterogeneity. The average fractal dimensions of the small and large pore-throats are 2.16 and 2.52, respectively, indicating greater complexity in the large pore-throat structures. The SEM-derived fractal dimension (D_SEM) reflects the diversity of pore shapes and the complexity of the micro-scale geometries. As the reservoir quality decreases, the pore structure becomes more complex, and the pore morphology exhibits increased irregularity. D_MIP and D_SEM values range from 2.21 to 2.49 and 1.01 to 1.28, respectively, providing a comprehensive quantitative characterization of multiple pore structure characteristics. The fractal dimension shows negative correlations with permeability, porosity, median radius, maximum mercury intrusion saturation, mercury withdrawal efficiency, and sorting factor, while showing a positive correlation with median and displacement pressures. Among these factors, the correlations with the maximum mercury intrusion saturation and sorting factor are the strongest (R² > 0.8). Additionally, the fractal dimension is negatively correlated with pore circularity and major axis length, but positively correlated with pore perimeter, aspect ratio, and solidity. A higher proportion of circular pores and fewer irregular or long-strip pores correspond to lower fractal dimensions. Furthermore, mineral composition influences the fractal dimension, showing negative correlations with feldspar, quartz, and chlorite concentrations, and a positive correlation with carbonate content. This study provides new perspectives for the quantitative characterization of pore structures in tight sandstone reservoirs, enhances the understanding of low-permeability formation reservoir performance, and establishes a theoretical foundation for reservoir evaluation and exploration development in the study area.

1. Introduction

Continuous advancements in oil and gas exploration have positioned unconventional energy sources, particularly tight sandstone reservoirs, as a central focus of the industry, highlighting their critical importance for future exploration and development [1,2,3]. Unlike traditional reservoirs, these oil and gas reservoirs exhibit suboptimal features, complex pore structures, limited connectivity, and pronounced heterogeneity, all of which considerably affect the reservoir’s storage capacity and flow characteristics [4,5,6]. Therefore, a thorough analysis of the micro-pore-throat structure of tight sandstone reservoirs is crucial for precise reservoir characterization and enhanced oil and gas development efficiency.

Fractal theory, introduced by Mandelbrot (1983), provides a statistical framework for characterizing the irregularity and self-similarity of intricate porous media [7]. Studies have shown that porous rocks exhibit self-similar pore structures that are consistent across various scales [8]. Therefore, the fractal dimension (D), an important indicator of pore system complexity, provides a reliable basis for assessing reservoir quality and conducting petrophysical analyses [9]. A higher fractal dimension typically indicates a more complex pore architecture. In recent years, fractal theory has been extensively utilized in petroleum exploration and production, particularly in the analysis of the micro-pore-throat structures of reservoirs [10,11]. In pore characterization, obtaining the fractal dimension using nuclear magnetic resonance T₂ spectra [12,13], nitrogen adsorption models [14,15], scanning electron microscopy (SEM) image analysis [16], and high-pressure mercury injection (HPMI) [17,18] has become a common approach. SEM image analysis allows for the direct examination of pore shape and structure, whereas HPMI offers advantages such as simplicity, cost-effectiveness, high precision, and extensive pore-throat identification capabilities [19,20]. Combining both methods facilitates a more comprehensive study of the fractal features and structural characteristics of pores. Researchers have quantitatively analyzed the fractal features and pore structures of sandstones [21,22], shales [23,24], coal rocks [25,26], and carbonates [27] by combining the HPMI and SEM. However, current SEM image analysis largely relies on manual operations, which are time-consuming, labor-intensive, and prone to subjectivity based on the researcher’s experience, making quantitative research weak and uncertain. Although general image processing software, such as Image-Pro and JMicro Vision, can assist in the analysis, they are not suitable for bulk processing or automated analysis of sandstone sample images [28,29]. With advancements in computer technology, deep learning-based image recognition techniques have significantly improved pore extraction and morphological analyses. However, most existing studies are limited to simple pore extraction, classification, or partial mineral identification, with limited attention to the quantitative characterization of pore structures and geometric parameters [30,31,32,33]. In addition, pore recognition in tight sandstone still faces several challenges: (1) tight sandstone pores have poor permeability, and their complex and diverse pore structures hinder effective image recognition; and (2) different study objects have varying applicability, requiring the selection of an appropriate learning model based on sample characteristics. For example, the fully convolutional network model is suitable for coal rock fracture identification [34], the Mask R-CNN model is suitable for rock pore identification [35], and the U-Net model is commonly employed for micro-pore extraction and identification [36]. In summary, previous studies have focused on traditional methods to extract pores from SEM images, and this is inefficient and not highly accurate. Although some studies have applied deep learning techniques, their effectiveness is limited, and different models are required for different regions. Moreover, the relationships between pore structure parameters, geometric parameters, mineral composition, fractal dimension, and reservoir quality in tight sandstone reservoirs require further investigation.

Based on the aforementioned challenges, this study examined the Chang 8 tight sandstone reservoir in the Jiyuan, Ordos Basin. Using SEM image-derived pore parameters and HPMI experimental data from 16 core samples, pore structures were extracted with an improved U-Net model to calculate and compare the two types of fractal dimensions. This study quantitatively characterizes the pore structure of tight sandstone and analyzes its heterogeneity in both planar and spatial domains. It further explores the correlations among the fractal dimension, reservoir quality, pore structure parameters, geometric parameters, and mineral composition. The findings reveal the geological significance of the fractal dimension in characterizing pore structures in continental tight sandstone reservoirs. This study provides precise, quantitative descriptions of pore characteristics in tight sandstone reservoirs, while presenting novel approaches and methodologies for reservoir evaluation and exploration.

2. Geological Setting

The Ordos Basin, China’s second-largest sedimentary basin, spans five provinces—Shaanxi, Gansu, Shanxi, Ningxia, and Inner Mongolia—covering an area of 2.5 × 10⁵ km² and containing an estimated 6.2 × 10¹² m³ of resources, offering significant exploration potential [37,38,39]. It comprises six major structural units: the Yimeng Uplift, Wei Bei Uplift, Tianhuan Depression, Western Margin Thrust Belt, Northern Shaanxi Slope, and Jinxi Folding Belt [40]. The study area, Jiyuan, is situated in the central-western Ordos Basin, covering 1305 km². It spans from Dunwa in the west to Haojianshan in the east, and from Shangwan in the north to Jiyuan in the south (Figure 1a). The confirmed petroleum reserves in the region amount to 8 × 10⁸ t, with an annual crude oil output of 7 × 10⁶ t, establishing it as the largest oil field in terms of both reserves and production within the Mesozoic strata of the Ordos Basin. The Chang 8 reservoir is the primary production target in this region. The proven favorable oil-bearing area spans 1500 km², with a wide distribution and an average single-well oil layer thickness of 15–20 m, providing favorable conditions for exploration and development [41,42,43].

Alternating layers of gray sandstones and black mudstones define the Chang 8 reservoir, which is located in the lower to middle portion of the Upper Triassic Yanchang Formation. The depositional environment consists of underwater distributary channels and interdistributary bays, representing a typical shallow-water delta system (Figure 1b) [44,45]. Casting thin section (CTS) analysis indicate that the Chang 8 reservoir consists predominantly of fine-grained feldspathic lithic sandstone and lithic feldspathic sandstone, with a smaller proportion of feldspathic sandstone (Figure 2). The clastic constituents mainly include quartz, feldspar, and lithic fragments. The quartz content is from 20.52% to 57.32%, averaging 32.18%; the feldspar content is from 19.95% to 57.58%, averaging 35.56%; and the lithic fragments are from 7.85% to 28.45%, averaging 21.75%. Overall, the Chang 8 reservoir in the study area exhibits favorable reservoir conditions and significant exploration potential. Its rock types and mineral composition significantly influence the pore structure and reservoir characteristics, providing geological evidence for further quantitative characterization of pore features.

Figure 1. (a) Location of the research region (Modified from Yang [46]). (b) Column diagram of the Chang 8.

Figure 1. (a) Location of the research region (Modified from Yang [46]). (b) Column diagram of the Chang 8.

3. Materials, Experiments, and Methods

3.1. Materials

This research examined 16 core samples collected from the Chang 8 reservoir in Jiyuan, Ordos Basin, China. All specimens were composed of fine-grained sandstones. The samples were subjected to oil washing, gas permeability testing, and porosity calculations using the weighing method to determine the reservoir’s physical parameters (

Table 1. Information on Experimental Samples.

Sample	Depth (m)	Diameter (cm)	Length (cm)	Porosity (%)	Permeability (10−3 µm2)	Lithology
X1	2218.63	2.50	5.20	9.29	0.24	Fine lithic feldspar sandstone
X2	2230.21	2.48	5.20	11.54	0.23	Fine lithic feldspar sandstone
X3	2208.42	2.50	5.10	9.08	0.17	Fine feldspar lithic sandstone
X4	2236.86	2.49	5.00	7.16	0.11	Fine lithic feldspar sandstone
X5	2255.65	2.50	5.20	12.40	0.21	Fine lithic feldspar sandstone
X6	2231.73	2.50	5.20	10.43	0.20	Fine feldspar lithic sandstone
X7	2252.71	2.50	5.20	5.65	0.08	Fine lithic feldspar sandstone
X8	2240.06	2.48	5.10	6.68	0.06	Fine lithic feldspar sandstone
X9	2213.66	2.50	5.00	7.50	0.09	Fine lithic feldspar sandstone
X10	2227.31	2.50	5.20	9.55	0.07	Fine feldspar lithic sandstone
X11	2206.42	2.50	5.20	9.99	0.06	Fine lithic feldspar sandstone
X12	2259.82	2.50	5.20	7.40	0.05	Fine lithic feldspar sandstone
X13	2260.54	2.48	5.00	6.52	0.06	Fine feldspar lithic sandstone
X14	2253.39	2.50	5.20	2.41	0.01	Fine feldspar lithic sandstone
X15	2261.07	2.50	5.20	7.04	0.02	Fine lithic feldspar sandstone
X16	2265.07	2.50	5.10	3.09	0.02	Fine feldspar lithic sandstone

). The samples were obtained from depths ranging from 2206.42 to 2265.07 m. Porosity values ranged from 2.4% to 12.4%, and the grade difference was 10, with an average of 7.86%, whereas permeability ranged from 0.008 × 10⁻³ µm² to 0.24 × 10⁻³ µm², and the grade difference was 0.232, with an average of 0.11 × 10⁻³ µm². A total of 200 high-resolution images were obtained through CTS and SEM analyses. HPMI experiments were conducted on all 16 samples to determine the microscopic pore-throat characteristics.

3.2. Experiments

3.2.1. HPMI

HPMI is a direct and efficient technique for assessing microporous structures and is widely employed in the evaluation of tight sandstone reservoirs [47]. In this study, cylindrical rock samples with a diameter of 2.5 cm were selected, ensuring that the surfaces were intact and crack-free. The experiment was conducted using the Auto Pore V9600 fully automatic mercury injection apparatus, which covers a measuring range of 5 nm to 1200 μm. Mercury was injected continuously, with a volume accuracy of less than 0.1 μL for both injection and withdrawal. The experimental procedures followed the national standard GB/T29171-2012. The smallest detectable pore-throat radius was 0.0036 μm, the highest capillary pressure was 206.82 MPa, and the maximum mercury inlet pressure was 96.45 MPa.

3.2.2. CTS and SEM

CTS, prepared using staining agents, enables the direct examination of pore architecture and mineral compositions in rock samples [48]. In this investigation, samples were sliced into 2 cm × 2 cm sections and stained under vacuum conditions. A Leica DM4500PFCHG-013 polarizing microscope was used to examine 16 thin sections of tight sandstone, following the national standard SY/T5368-2000. SEM is widely used to analyze sample morphology at a high resolution and to characterize pore structures and mineral compositions. It can be used to observe the microscopic pore-throat development characteristics of the reservoir [49]. The JSM-7500F field emission scanning electron microscope was used in this study. The secondary electron image resolution of the scanning electron microscope was 1 nm, and the magnification was 20–300,000×. All experiments were conducted at the State Key Laboratory of Continental Evolution and Early Life, Northwest University.

3.3. Methods

3.3.1. Fractal Dimension Based on HPMI

Fractal theory has evolved into a mature framework, enabling the quantitative characterization of pore types, pore structures, and reservoir physical properties [50]. Typically, the fractal dimensions calculated using the HPMI method range between 2 and 3. A larger fractal dimension indicates greater complexity in the pore structure and stronger reservoir heterogeneity [51]. In this study, the fractal dimensions of the pore-throats were calculated using HPMI data from 16 samples.

Fractal geometry theory states that the number of objects N(r) at a specific scale r adheres to a power-law relationship:

$$N(r)\propto r^{-D}$$

(1)

It was assumed that the reservoir pores exhibited fractal characteristics. The pore-throat radius is the linear scale r of the measurement, the number of pores is converted based on the pore-throat radius r, and the mercury inlet volume V_Hg is N (r). For HPMI, the number of pores N (r) can be obtained using the capillary model, as follows:

$$N(r)={\displaystyle \frac{V_{Hg}}{\pi r^{2}l}}$$

(2)

Combining Equations (1) and (2), we obtain:

$${\displaystyle \frac{V_{Hg}}{\pi r^{2}l}}\propto r^{-D}$$

(3)

$$V_{Hg}\propto r^{2-D}$$

(4)

where l is the length of capillary, µm; V_Hg is the volume of mercury, µm³; r is the radius of pore-throat, µm.

According to the Young–Laplace equation:

$$P_c={\displaystyle \frac{2\sigma \cos \theta }{r}}$$

(5)

where P_c is the mercury injection pressure, MPa; σ is the interfacial tension, N/m; and θ is the contact angle, °.

Substituting Equation (5) into Equation (4) yields

$$V_{Hg}\propto P_c^{D-2}$$

(6)

Mercury saturation S_Hg in the sample is defined as

$$S_{Hg}={\displaystyle \frac{V_{Hg}}{V_p}}$$

(7)

Assuming that l is constant, from Equations (6) and (7), the relationship between S_Hg and P_c is obtained as

$$S_{Hg}=\alpha P_c^{D-2}$$

(8)

where S_Hg is the mercury saturation, %; V_p is the total pore volume of the sample, µm³; and α is a constant, indicating that the mercury saturation in the rock sample follows a power-law relationship with the capillary pressure

Taking the logarithm of both sides of Equation (8):

$$\ln S_{Hg}=(D-2)\ln P_c+C$$

(9)

This suggests that if the pore structure of the reservoir rock samples has fractal features, lnS_Hg and lnP_c demonstrate a linear correlation in a double-logarithmic coordinate system. Here, C represents the intercept, and D represents the fractal dimension, which may be obtained from the slope of the line.

3.3.2. Enhanced U-Net Model

U-Net, proposed by Ronneberger in 2015, is a deep learning model based on convolutional neural networks [52]. It achieves efficient image segmentation through skip connections and a fully convolutional network decoding stage. In this study, DropBlock and Batch Normalization layers were integrated into the convolutional blocks of the original U-Net model to construct an improved reconstruction block, enhancing both recognition accuracy and computational speed (Figure 3b). DropBlock is a regularization technique that, unlike traditional Dropout, randomly masks blocks of neurons in the network, reducing redundant connections and improving the model’s generalization ability. Batch Normalization is an essential technique for regularization and accelerating training. Normalizing the input distribution to the intermediate layers improves both the training speed and stability of deep networks. Additionally, the skip connections in the original U-Net model were replaced with a feature pyramid network, merging features from different resolutions to enhance feature extraction, thus forming an improved U-Net architecture (Figure 3a).

The primary operational steps were as follows: (1) Dataset preprocessing: The original SEM images were cropped to 512 × 512 pixels using Adobe Photoshop™ for computer recognition. The dataset was then partitioned into training and test sets in a 7:3 ratio. ImageJ 1.54d software was used to identify the training set and convert it to grayscale. In deep learning, larger and more diverse training samples improve the accuracy. Therefore, the Python Imgaug data augmentation library was used to apply elastic transformations, random cropping, scaling, and rotation to increase the diversity of the training dataset and improve model robustness. During the training, image augmentation techniques, such as rotate (limit = 30, p = 0.5), elastic transform (alpha = 50, sigma = 10, p = 0.2), and horizontalflip (p = 0.5), were applied to enhance the diversity of the training dataset and improve the model’s robustness. (2) Backbone feature extraction: A 512 × 512 image was input with two 3 × 3 convolutions and corresponding 2 × 2 max pooling at each step. The initial number of feature channels was 64, which doubled after each downsampling step, resulting in five effective feature layers. (3) The feature values at five depths were input into a feature pyramid network (Figure 3c). The network builds a feature fusion path with bottom-up, top-down, and lateral connections, along with convolutional fusion, to combine feature maps at different scales. Upsampling was performed using 2 × 2 convolutions, reducing the number of feature channels by half at each step. (4) Prediction: The final effective feature layers are used to classify and identify each feature point.

The model was trained and evaluated on a deep learning workstation running Windows 10, equipped with a 13th Gen Intel(R) Core(TM) i9-13980HX @2.20 GHz processor, 128 GB of RAM, and NVIDIA GeForce RTX 3060 GPU. The deep learning model was built in Python 3.12, using the PyTorch 1.7 framework. During training, the Adam optimizer was employed for the loss function. The learning rate was set to 0.0001 to ensure model stability during the learning process and minimize oscillation near the optimal solution. The batch size was configured at 8, and the epoch was set to 100, ensuring that the model had sufficient iterations to learn the training data to gradually converge to a better state. This model is particularly suitable for image identification applications in fine-grained sedimentary rocks with complex microstructures. Compared to other models, it performs better and can automatically extract pore geometric parameters from SEM images in batches [53,54,55,56,57]. The model’s IOU reaches 0.91. The AP is comparatively high, reaching 0.945, indicating strong performance in pore recognition. The model achieves a precision of 0.951, an MAE of 0.108, and a Dice score of 0.872.

3.3.3. Fractal Dimension Based on SEM

Tight sandstone, a porous medium in sedimentary rocks, exhibits pronounced fractal characteristics in its pores. SEM images revealed the pore features of the tight sandstone, with the extracted pore boundaries being closed. Because the pores captured by SEM are 2D images, the fractal dimension derived from the SEM images cannot exceed 2. According to Voss, the fractal dimension of the pore morphology can be determined by utilizing the relationship between the pore area and the perimeter [58]. The relationship between the pore area and the perimeter for pores exhibiting fractal properties is expressed as

$$\lg P={\displaystyle \frac{D}{2}}\lg A+C$$

(10)

where P is the pore perimeter (µm) extracted from the SEM images, A is the pore area (µm²), D is the fractal dimension, and C is a constant.

In this study, deep learning technology was used to extract pore parameters from 16 samples, yielding 7258 valid pores. The geometric parameters of these pores were analyzed, and each sample’s fractal dimension was calculated using Equation (10).

4. Results

4.1. Pore Structure Characterization

4.1.1. Pore Structure Characteristics Based on HPMI

Based on the analysis of the physical property parameters and HPMI data from 16 samples in the study area, the samples were categorized into three types (

Table 2. Classification criteria for typical samples of Chang 8 in the study area.

Group	Sample Number	Φ (%)	K (10−3 µm2)	Displacement Pressure	Median Radius	Median Pressure	Coefficient of Variation	Sorting Factor	Skewness	Maximum Mercury Saturation (%)	Mercury Withdrawal Efficiency (%)
I	X1	9.29	0.24	0.95	0.11	8.35	16.36	2.15	0.17	92.49	41.72
	X2	11.54	0.23	0.61	0.12	8.11	14.26	2.14	0.33	89.89	32.48
	X3	9.08	0.17	0.76	0.14	5.77	16.95	2.09	0.44	86.83	39.29
	X4	7.16	0.11	0.69	0.14	5.39	16.67	2.18	0.46	87.39	38.44
	X5	12.40	0.21	0.80	0.11	4.36	17.84	2.41	1.68	91.51	40.71
	X6	10.43	0.20	0.73	0.15	4.91	16.81	2.23	1.58	89.98	37.57
II	X7	5.65	0.08	1.19	0.09	7.55	15.45	2.03	0.43	88.32	32.81
	X8	6.68	0.06	1.54	0.05	8.76	13.99	1.85	0.50	85.08	36.76
	X9	7.50	0.09	0.96	0.09	6.67	14.25	1.88	0.60	84.45	32.50
	X10	9.55	0.07	0.78	0.10	9.80	14.69	1.89	0.65	85.33	38.90
	X11	9.99	0.06	1.51	0.10	11.48	15.85	1.91	0.45	82.62	39.21
III	X12	7.40	0.05	2.26	0.03	27.06	8.42	0.96	−0.02	75.80	26.21
	X13	6.52	0.06	4.40	0.02	52.41	8.54	1.37	−0.05	77.52	23.22
	X14	2.41	0.01	0.95	0.14	90.79	4.94	1.28	0.48	73.45	24.99
	X15	7.04	0.02	2.29	0.02	35.55	9.26	1.60	0.05	79.61	29.71
	X16	3.09	0.02	2.86	0.02	56.36	8.96	1.83	0.01	75.90	28.57

). Type I samples exhibited favorable physical qualities, with average permeability and porosity values of 0.21 × 10⁻³ μm² and 9.98%, respectively. The capillary pressure curve displayed an elongated plateau, skewed toward the bottom left. The mean displacement pressure and median pressure were moderate at 0.76 MPa and 6.15 MPa, respectively. The mean sorting factor was 2.20, signifying satisfactory sorting quality and a relatively uniform throat size distribution. The throat type was sheet-like (Figure 4f). The pores were mainly intergranular and feldspar dissolution pores, with some affected by compaction and dissolution, forming irregular and long-strip pores. Type II samples exhibited moderate physical properties, with an average porosity of 7.87% and a permeability of 0.07 × 10⁻³ μm². The capillary pressure curve displayed a slow increase followed by a clear horizontal plateau. The average displacement pressure and median pressure exceeded those of the Type I samples, recorded at 1.20 MPa and 8.85 MPa, respectively. The mean sorting factor was 1.91, indicating moderate sorting. The pores were primarily residual intergranular and feldspar dissolution pores, predominantly long strips in shape. A small number of irregular micropores were observed, along with constricted throats (Figure 4b,e). Type III samples had the least advantageous physical qualities, averaging permeability of 0.03 × 10⁻³ μm² and porosity of 5.29%, both of which were markedly inferior to those of Type I and II samples. The horizontal platform of the capillary pressure curve was not obvious, and the curve was steep. The average displacement and median pressures were the largest, at 2.55 MPa and 52.43 MPa, respectively. The average sorting factor was the lowest at 1.41, indicating poor sorting. The pores mainly consisted of intercrystalline pores and micropores, with intercrystalline pores forming between clay minerals, such as chlorite. These pores were characterized by a complex and variable structure with poor connectivity. Many small throats with poor storage capacities and high heterogeneities were observed (Figure 4c).

4.1.2. Pore Structure Characteristics Based on SEM

SEM images provide pore-shape-related parameters that are essential for quantitatively assessing pore structure types, distribution characteristics, and heterogeneity. In this study, 150 SEM images were acquired from 16 samples. Using an enhanced U-Net deep learning model, the geometric parameters of each pore were automatically extracted from the SEM images, including the perimeter, circularity, major axis, aspect ratio, and solidity (

Table 3. Results of Pore Geometry Parameters Extracted by Deep Learning.

Group	Sample Number	Φ (%)	K (10−3 µm2)	Perimeter (µm)	Circularity	Major Axis (µm)	Aspect Ratio	Solidity
I	X1	9.29	0.24	66.64	0.56	187.25	1.57	0.34
				6.37~659.15	0.31~0.97	2.84~394.5	1.01~5.78	0.06~0.45
	X2	11.54	0.226	113.44	0.53	156.85	1.33	0.26
				2.69~856.46	0.22~0.96	1.334~358.3	1.09~4.95	0.05~0.37
	X3	9.08	0.174	57.08	0.49	131.30	1.60	0.43
				4.36~417.35	0.14~0.94	1.34~256.78	1.06~6.25	0.08~0.49
	X4	7.16	0.11	89.68	0.47	122.65	2.16	0.45
				9.03~874.24	0.079~0.93	2.07~173.16	1~3.05	0.04~0.57
	X5	12.4	0.212	129.56	0.51	184.10	1.52	0.21
				6.27~958.28	0.079~0.95	2.84~294.5	1.01~3.78	0.05~0.43
	X6	10.43	0.199	125.88	0.51	181.95	2.05	0.36
				8.34~946.83	0.07~0.93	1.8~276.9	1.05~4.92	0.10~0.38
II	X7	5.65	0.075	137.32	0.40	91.90	2.415	0.55
				9.38~1176.45	0.097~0.86	1.28~109.56	1.05~2.10	0.36~0.88
	X8	6.68	0.06	130.8	0.36	81.90	2.29	0.63
				10.69~1208.68	0.052~0.88	1.21~112.31	1.09~4.13	0.26~0.84
	X9	7.5	0.085	112.08	0.47	102	1.52	0.57
				14.83~1157.15	0.026~0.91	0.98~168.51	1.09~3.6	0.33~0.74
	X10	9.55	0.068	125.64	0.39	142.65	1.89	0.42
				12.34~1298.58	0.092~0.89	0.93~143.5	1.09~2.65	0.36~0.69
	X11	9.99	0.057	434.96	0.37	102.2	1.92	0.48
				9.34~1498	0.067~0.83	1.02~150.6	1.01~3.49	0.37~0.73
III	X12	7.4	0.053	497.92	0.34	105.6	2.37	0.73
				8.04~1343.24	0.058~0.87	1.05~129.61	1.03~5.54	0.36~0.95
	X13	6.52	0.059	399.76	0.35	68.90	2.78	0.67
				5.34~1576.17	0.064~0.82	0.89.48~89.9	1.05~4.17	0.27~0.96
	X14	2.41	0.008	398.24	0.32	80.35	2.55	0.68
				6.31~1035.56	0.047~0.82	0.95~96.96	1.01~5.86	0.29~0.95
	X15	7.04	0.017	474.24	0.33	77.55	2.35	0.71
				7.56~1498.47	0.06~0.79	0.45~92.82	1.09~4.6	0.32~0.93
	X16	3.09	0.022	289.68	0.34	62.10	2.21	0.70
				5.83~1312.49	0.098~0.72	0.34~88.73	1.14~5.23	0.27~0.82

). The mean values of these parameters were then calculated for each sample. The analysis revealed that the pore geometric parameters of the tight sandstone reservoir samples exhibited significant variation and uneven distribution, indicating substantial reservoir heterogeneity and complex pore structures. There were six Type I samples (X1–X6). The pore perimeter varied between 57.08 μm and 129.56 μm, averaging 97.05 μm. Circularity ranged from 0.47 to 0.51, with an average of 0.51. The major axis ranged between 122.65 μm and 187.25 μm, averaging 160.68 μm. The aspect ratio varied from 1.33 to 2.16, with a mean of 1.71. Solidity varied from 0.21 to 0.45, with a mean of 0.34. There were five Type II samples (X7–X11). The pore perimeter ranged from 112.08 μm to 434.96 μm, with an average of 188.16 µm. The average circularity was 0.40, with a range of 0.39 to 0.47. The major axis ranged from 81.9 μm to 142.65 μm, with a mean of 104.13 µm. The average aspect ratio varied from 1.52 to 2.41, with an average of 2.01. The average solidity was 0.53, with a range of 0.42 to 0.63. There were five Type III samples (X12–X16). The pore perimeter ranged between 289.68 um and 497.92 um, with an average of 411.97 um. Circularity varied from 0.32 to 0.35, with an average of 0.34. The major axis ranged between 62.1 um and 105.6 um, with a mean of 78.3 um. The aspect ratio varied from 2.21 to 2.78, with an average of 2.45. Solidity ranged between 0.67 and 0.73, averaging 0.70. The data indicated relatively high average values for the perimeter, major axis, aspect ratio, and solidity across all samples, whereas the average circularity remained comparatively low. This indicates that tight sandstone pores are primarily irregular, exhibiting a scarcity of circular pores, which aligns with the low porosity and permeability characteristic of tight sandstone. Longitudinal analysis revealed that Type I samples exhibited the highest average circularity and major axis, followed by Type II and Type III. This suggests that reservoir quality is positively correlated with both circularity and the major axis. The larger these parameters, the better the pore permeability. The greater the pore circularity, the closer the pore shape is to that of a circle. Circular pores typically exhibit a uniform distribution, enabling better connectivity and fluid flow. The major axis refers to the long axis of the outer ellipse of the pore, which directly affects the pore size and connectivity. When the length of the major axis increased, the pore size also increased, and the connectivity was enhanced. Conversely, Type I samples displayed the lowest average pore perimeter, aspect ratio, and solidity, with Type II showing intermediate values and Type III exhibiting the highest values. This indicates that the reservoir quality is inversely correlated with the pore perimeter, aspect ratio, and solidity. The smaller these parameters, the higher the pore permeability. A larger pore perimeter indicates a more complex pore structure, increasing the fluid flow path tortuosity and reducing permeability. The aspect ratio, which represents the proportion of the long-to-short axis length of the pore’s outer ellipse, affects fluid seepage; higher values indicate narrower pores and longer seepage channels, which impede fluid flow. Solidity indicates the degree of pore inward curvature; higher values correspond to more concave pore shapes, reduced circularity, and restricted inter-pore fluid flow.

Complex pore networks, characterized by multiple types and cross-scale variations, determine the conditions for tight oil occurrence. The configuration of pore structures in tight sandstone reservoirs is a critical criterion for evaluating tight oil accumulation and serves as a fundamental factor influencing reservoir physical properties. Based on the pore parameters and shapes identified by the enhanced U-Net model, the pore shapes are classified into three categories: circular, random irregular, and long-strip pores (Figure 5 and Figure 6). Circular pores display regular shapes, high circularity (0.65–0.95), aspect ratios close to 1 (1.15–1.3), and low solidity (0.1–0.35). These pores are primarily found in primary intergranular pores, soluble minerals, and isolated pores in the cement. Their development is controlled by weak compaction, uniform dissolution, and the sealing effect of the cement. In contrast, the random irregular pores display diverse shapes, often resembling triangles, polygons, honeycomb patterns, and grids. They are characterized by low circularity (0.3–0.6), relatively large aspect ratios (1.35–1.70), and high solidity (0.4–0.6). These pores are found in both brittle and clay minerals and are mainly influenced by the original sedimentary structures, dissolution, and compaction. Long-strip pores are characterized by being narrow and slender, with the lowest circularity (0.1–0.3), highest aspect ratio (greater than 2.4), and greatest solidity (0.7–1.0). This type of pore predominantly occurs in the intergranular spaces of brittle minerals, such as kaolinite, quartz, and feldspar. It also appears in highly compacted intergranular pores formed by the directional arrangement of microfractures and flaky minerals, such as mica and chlorite.

4.2. Fractal Characterization

4.2.1. Fractal Dimensions Obtained from HPMI Data

Fractal analysis was conducted using HPMI data from 16 sandstone samples based on the lnS_Hg-lnP_c relationship plot (Figure 7), where the slope (k = D-2) indicates the fractal dimension. The results indicate that all samples show distinct segmentation in their pore fractal characteristics. The slope of the first section is the largest, corresponding to a fractal dimension between 4.0 and 9.0. The slopes of the second and third sections are small, with fractal dimensions ranging from 2.0 to 3.0. Pores are generally considered to exhibit fractal characteristics when the fractal dimension is within the range of 2.0 to 3.0. When it exceeds 3.0, the pores do not exhibit these characteristics. Therefore, the first segment is considered invalid and cannot serve as a metric for assessing the pore structure of the sample. The pore structure of tight sandstones exhibits distinct binary properties [59]. When the pore-throat radius is smaller than the peak pore-throat radius, the pore structure resembles a capillary type, where the pore radius is close to the throat radius, resulting in a small slope for the lnP_c and lnS_Hg fitting line. The mercury intrusion volume increases slowly with the pore-throat radius and is determined by the throat radius. At this stage, the fractal dimension of the pore-throat is between 2 and 3, and the pore-throat exhibits characteristics between two-dimensional and three-dimensional extension, where the capillary length (l) increases with the capillary radius (r). However, the growth rate of l is slower than that of r. The pore structure exhibits some degree of self-similarity, indicating fractal characteristics. When the pore-throat radius exceeds the peak pore-throat radius, the pore structure resembles a bead-chain model, where the pore radius is significantly larger than the throat radius, and the slope of the lnP_c and lnS_Hg fitting line is larger. As the pore-throat radius increases, the mercury intrusion volume increases rapidly, and the contribution of the pore to the pore-throat volume exceeds that of the throat. At this point, the fractal dimension of the pore-throat is greater than 3, and the pore-throat exhibits three-dimensional non-geometric extension, lacking fractal characteristics. The distribution of the throat radius in each sample is uneven, with varying peak values that are closely related to permeability and porosity. Specifically, Type I samples exhibit the largest peak throat radius at approximately 0.39 µm, corresponding to a capillary pressure of 1.85 MPa. Type II samples have a smaller peak throat radius than Type I samples, approximately 0.22 µm, corresponding to a capillary pressure of 3.57 MPa. Type III samples have the smallest peak throat radius at approximately 0.06 µm, corresponding to a maximum capillary pressure of 11.67 MPa. The second and third sections of the fractal plots for the Type I and II samples show obvious segmentation. The overall fractal dimension of the macropores and micropores ranges between 2.11 and 2.7, demonstrating a dual-fractal characteristic (Figure 4). The inflection point occurs at P_c = 6.82 MPa, distinguishing small pores (r < 0.1 µm) from large pores (r > 0.1 µm). The porosity ratios of the small and large pores were computed individually, and the overall fractal dimension (D_MIP) of the whole pore space was derived from the weighted average of the porosity of each pore space (Equation (11)). For Type I samples (X1–X6), the fractal dimension (D₁) for small pores varies between 2.11 and 2.19, with a mean of 2.15. The correlation factor (R²) varies from 0.937 to 0.977, with a mean of 0.964. The fractal dimension (D₂) for large pores varies between 2.34 and 2.47, with a mean of 2.41. The R² values range from 0.963 to 0.986, with an average of 0.979. D_MIP values vary from 2.21 to 2.28, with an average of 2.24. For Type II samples (X7–X11), D₁ for small pores ranges from 2.12 to 2.24, averaging 2.18. The R² values range from 0.953 to 0.992, with an average of 0.973. D₂ for large pores extends from 2.58 to 2.70, with an average of 2.65. The corresponding R² values range from 0.987 to 0.994, with an average of 0.990. D_MIP extends from 2.31 to 2.37, with a mean of 2.34. For the Type III samples (X12–X16), the second and third segments of the fractal curve do not show distinct segmentation, and no obvious inflection point is observed. The fitted curve is an approximate straight line, with R² values ranging between 0.989 and 0.996, and a maximum average of 0.993. D_MIP values range from 2.39 to 2.50, averaging 2.44, with most values exceeding 2.40. This is attributed to the poor permeability and porosity of Type III reservoirs, which are dominated by small pores with small pore-throat radius. These reservoirs exhibit relatively simple pore structures and poor overall connectivity, thereby exhibiting a single fractal characteristic. D_MIP increases sequentially from Type I to III reservoirs, indicating that declining reservoir quality corresponds to increased pore structure complexity, greater heterogeneity, and reduced pore connectivity. Furthermore, the fact that D₂ exceeds D₁ suggests that large pore-throat structures are more complex, aligning with previous research findings [60,61,62,63].

$$D_{MIP}=D_1\times {\displaystyle \frac{{\phi }_1}{{\phi }_1+{\phi }_2}}+D_2\times {\displaystyle \frac{{\phi }_2}{{\phi }_1+{\phi }_2}}$$

(11)

where D₁ and D₂ are the fractal dimensions corresponding to the small and large pore sections, respectively; φ₁ and φ₂ are the porosity proportions of the small and large pores, respectively.

4.2.2. Fractal Dimensions Obtained from SEM

According to fractal theory, the fractal dimension calculated from the SEM images should range between 1 and 2. The calculated results were within this range, indicating that they possessed fractal geometric significance. Using deep learning methods to extract pore structures from the SEM images, a double-logarithmic coordinate plot of the pore area (A) and perimeter (P) was created for the 16 sandstone samples (Figure 8). The two parameters showed a strong linear relationship (R² > 0.9), with the overall fractal dimension (D_SEM) ranging from 1.01 to 1.28 and an average of 1.14. This demonstrates that the pore morphology of the experimental samples exhibited clear fractal characteristics. For Type I samples (X1–X6), D_SEM ranged from 1.01 to 1.08, averaging 1.04. For Type II samples (X7–X11), it ranged from 1.15 to 1.17, averaging 1.15. For Type III samples (X12–X16), D_SEM varied from 1.19 to 1.28, with a mean of 1.24. The findings demonstrate that Type I reservoir samples possess the lowest D_SEM values, followed by Type II, with Type III having the largest values. This suggests that deteriorating reservoir quality correlates with increasing pore structure complexity and irregular pore shape.

5. Discussion

5.1. Comparison of Fractal Dimensions from HPMI and SEM Data

As discussed in Section 4.2.1, the effectiveness of the fractal dimensions derived from the HPMI data strongly correlates with the pore-throat radius, owing to capillary forces during the experiment. When the pore-throat radius is smaller than the peak radius, the pore structure approximates the capillary model, with the pore radius approaching the throat radius. The mercury intrusion volume increases slowly as the pore-throat radius increases, with the intrusion volume dominated by the throat radius [64]. At this stage, the D_MIP values range from 2.21 and 2.49, indicating a certain degree of self-similarity among pores and obvious fractal characteristics. When the pore-throat radius exceeds the peak radius, the D₀ values range from 4.05 to 8.82, which is substantially greater than 3, implying that the pore structure lacks fractal characteristics. During the HPMI process, the high pressure can cause deformation or compression of the pores. As a result, the actual pore structure becomes simpler than that obtained through mercury intrusion, leading to an underestimation of the fractal dimension. Moreover, due to the limitations of HPMI imposed by the maximum intrusion pressure, smaller pore-throats cannot be detected, and some tiny pore-throats are overlooked. This may lead to an underestimation of the complexity of the pore structure and the intricate connectivity between pores, ultimately affecting the accuracy of the fractal dimension.

In contrast, SEM images can provide a direct and comprehensive view of pore morphology and geometric parameters, with their measurement range not limited by the pore-throat radius or pressure factors. The D_SEM values range from 1.01 to 1.28, effectively reflecting the complexity and diversity of the pore morphology. However, the SEM method has its limitations: it cannot quantify pore-throat size distributions and often overlooks pore connectivity features. The observed differences between D_MIP and D_SEM are primarily due to differences in their underlying theoretical principles and mathematical models. The HPMI-derived fractal model is based on variations in the capillary pressure curve, primarily reflecting the connectivity and permeability of the pores. The SEM-derived fractal model is based on changes in pore morphology and size (such as pore area and perimeter), primarily reflecting the pore morphology and micro-geometric features.

In summary, although both the HPMI and SEM methods have advantages and disadvantages, and their respective fractal dimensions fall within different ranges, they illuminate the complexity and heterogeneity of pore structures at varying scales. Therefore, the combined use of HPMI and SEM data enables a more comprehensive quantitative characterization of the multiple features of the pore structure, providing strong support for advanced studies on the pore properties of tight reservoirs.

5.2. Relationship Between D and Pore Structure Parameters

Fractal dimension is closely correlated with reservoir heterogeneity and pore structure complexity, significantly influencing the reservoir’s physical properties. Typically, a larger fractal dimension indicates greater reservoir heterogeneity, poorer pore connectivity, more complex pore-throat structures, and diminished physical properties. The results show that both D_SEM and D_MIP exhibit strong negative correlations with porosity and permeability (Figure 9a,b). As the fractal dimension increases, both porosity and permeability decrease, indicating that complex pore structures with high fractal dimensions reduce rock permeability. Conversely, samples with large porosities, owing to the presence of large primary or dissolution pores, exhibit better pore connectivity and simpler pore structures. The median radius, indicative of the pore radius at 50% saturation of the non-wetting phase, may be estimated as the mean pore radius of the sample. It exhibits an inverse association with the fractal dimension (Figure 9c). This is because as the pore-throat radius increases, the reservoir pore-throat distribution becomes more concentrated, resulting in a larger storage space and more regular pore surfaces. Consequently, the reservoir’s pore structure becomes less complex, heterogeneity decreases, and physical properties improve. Both the maximum mercury saturation and mercury withdrawal efficiency, which reflect inter-pore connectivity, show significant negative correlations with the fractal dimension (Figure 9d,e). This indicates that complex pore structures affect the mercury intrusion and withdrawal processes, leading to a decrease in fluid permeability and deterioration in the physical properties of the reservoir. A higher fractal dimension indicates a more complex, finer, and irregularly structured pore system, resulting in poorer connectivity between pores. This prevents the mercury that enters the rock sample from being completely expelled, thereby reducing the mercury withdrawal efficiency. The sorting factor, which reflects the consistency of the pore-throat size distribution, shows a strong negative correlation with the fractal dimension (Figure 9f). It shows that the better the sorting of tight sandstone, the simpler the pore structure and the lower the fractal dimension. The median pressure, which refers to the capillary pressure corresponding to 50% saturation of the non-wetting phase, shows a positive correlation with the fractal dimension. A higher median pressure implies a denser rock sample with more complex pore structures, thus a higher fractal dimension (Figure 9g). Similarly, the displacement pressure, which refers to the capillary pressure corresponding to the maximum connected pore in the pore system and serves as a key indicator of the performance of sandstone reservoirs, shows a strong positive correlation with the fractal dimension. A higher fractal dimension indicates a more complex pore structure and increased displacement pressure (Figure 9h).

In conclusion, the fractal dimension demonstrates a significant correlation with the pore structure parameters of the reservoir. It effectively reflects the complexity and heterogeneity of the pore space. Lower fractal dimensions indicate smoother pore surfaces, more uniform pore distribution, higher connectivity, and reduced reservoir heterogeneity, resulting in greater storage capacity and permeability. This study reveals that maximum mercury saturation and the sorting factor exhibit the strongest correlation with the fractal dimension (R² > 0.8). These two factors, representing pore interconnectivity and uniformity of the pore-throat size distribution, exert the most significant influence on the fractal dimension. Additionally, the complexity of the reservoir pore architecture is influenced by multiple variables, including median pressure, displacement pressure, median radius, and mercury withdrawal efficiency.

5.3. Relationship Between D and Pore Geometry Parameters

Figure 10 shows the relationship between the fractal dimension and pore geometric characteristics. A strong negative correlation was observed between the fractal dimension and both the circularity and length of the major axis. Increased circularity signifies that the pore shape more closely approximates a circle, and circular pores generally exhibit a more uniform distribution, leading to enhanced connection and fluid flow. The length of the major axis, which denotes the principal axis of the circumscribed circle of the pore, affects pore connectivity and fluid flow paths. An augmentation in main axis length corresponds with increased pore size and improved connectivity among pores. Therefore, when the circularity and major axis length increase, the reservoir pore structure becomes more simplistic, resulting in a reduced pore fractal dimension. In contrast, solidity has a positive association with the fractal dimension. Solidity refers to the degree of concavity and convexity of the pores. The stronger the solidity, the more pronounced the concave pore shape, resulting in a lower circularity and an increased complexity of the pore configuration. The pore perimeter also exhibits a positive correlation with the fractal dimension. A longer perimeter typically indicates more complex pore edges with additional curved channels, resulting in a more intricate pore structure and reduced pore connectivity. Lower reservoir permeability is associated with higher levels of heterogeneity. The aspect ratio had a positive connection with the fractal dimension. Increased aspect ratios result in narrower pores, reduced pore size uniformity, and elevated fractal dimensions, consequently decreasing reservoir permeability. Overall, the pores in tight sandstones tend to have longer perimeters, lower circularities, and greater solidities, which correspond to larger fractal dimensions. This demonstrates the high heterogeneity and complex pore structure of these reservoirs.

5.4. Relationship Between D and Pore Morphology

Based on the classification of pore shape features described in Section 4.1.2, the proportions of different pore morphologies, along with D_MIP and D_SEM, were statistically analyzed for each sample (Figure 11). This study found that pore shapes and fractal dimensions vary across reservoir types. Overall, circular pores constituted a relatively small proportion (21.05%) of the three reservoir rock sample types, whereas irregular pores (45.74%) and long-strip pores (33.21%) constituted a larger proportion. The overall fractal dimensions were relatively high (average D_MIP = 2.34; average D_SEM = 1.14). These findings indicate that the tight sandstone reservoirs in the study area exhibited complex pore structures, predominantly characterized by irregular pores. Poor pore connectivity and significant heterogeneity were the main factors contributing to poor reservoir properties. A vertical comparison among the reservoir types showed that Type I reservoirs (X1–X6) had the lowest fractal dimensions (average D_MIP = 2.24; average D_SEM = 1.04). Circular pores accounted for the largest proportion of these samples (average 26%), whereas irregular pores (average 47.83%) and long-strip pores (average 26.17%) had smaller proportions. Type II reservoir samples (X7–X11) exhibited higher fractal dimensions than Type I (average D_MIP = 2.34; average D_SEM =1.15). In these samples, the proportion of circular pores was smaller than that in Type I (average 20.6%), whereas the proportions of irregular pores (average 50.4%) and long-strip pores (average 29%) were slightly higher than those in Type I reservoirs. Type III reservoir samples (X12–X16) had the highest fractal dimensions (average D_MIP = 2.44; average D_SEM = 1.24). The proportion of circular pores was the lowest in these samples, an average of 11.2%, which was much smaller than that in Types I and II, whereas the proportions of irregular pores (average 52.6%) and long-strip pores (average 36.2%) continued to increase. In summary, the fractal dimension gradually increases as circular pores decrease and irregular and long-strip pores increase. This results in more complex pore structures, reduced connectivity, increased heterogeneity, and poor reservoir properties. Therefore, the reservoir quality can be quantitatively assessed by analyzing the distribution of pore shape characteristics.

A horizontal comparison revealed that the pore shape proportions influenced the fractal dimension. In Type I reservoirs, sample X5 had the lowest fractal dimension (D_MIP = 2.21, D_SEM = 1.01), with the highest proportion of circular pores (35%) and the lowest proportion of long strip pores (17%). In Type III reservoirs, sample X15 exhibited the lowest fractal dimension (D_MIP = 2.39, D_SEM = 1.19), with circular pores accounting for the largest proportion (17%) and irregular pores accounting for a relatively smaller proportion (46%). This suggests that the presence of more circular pores—indicating better circularity and simpler pore structures—correlates with lower fractal dimensions. Conversely, a higher proportion of irregular and long-strip pores— indicating complex structures and poor connectivity—correlates with higher fractal dimensions. Additionally, the pore shape appears to have a greater influence on D_SEM than on D_MIP. For instance, Type II sample X8 had the highest D_SEM (1.17), with the lowest proportion of circular pores (12%) and higher proportions of irregular (59%) and long-strip pores (29%). Similarly, the Type III sample X14 had the highest D_SEM (1.28), with only 6% circular pores and high proportions of irregular (64%) and elongated pores (30%). The relationship between circularity and each fractal dimension (Figure 10a) showed that circularity correlated more strongly with D_SEM (R²_SEM = 0.83) than with D_MIP (R²_MIP = 0.68). This is because the D_SEM is calculated directly from the geometric parameters of the pores, such as the pore area and perimeter, which are directly related to the pore shape. In contrast, the D_MIP is derived using a mathematical model based on mercury pressure–volume relationships and segmented fitting of the intrusion curve, which cannot directly quantify pore boundary complexity.

5.5. Relationship Between D and Mineral Composition

Differences in the mineral composition directly influence the sedimentation and diagenetic processes of a reservoir, which is reflected in the heterogeneity of its pore structure. The fractal dimension signifies the intricacy and variability of the pore architecture. The examination of the link between mineral composition and fractal dimension (Figure 12) demonstrated a significant negative relationship between quartz concentration and fractal dimension (R² > 0.6): a higher quartz content corresponds to a lower fractal dimension. As a key framework mineral in tight sandstones, a higher quartz content enhances the sandstone’s resistance to compaction, thereby preserving intergranular pores and improving pore-throat connectivity. This leads to reduced heterogeneity and complexity. Feldspar content exhibited a weak negative correlation with the fractal dimension (R² < 0.5), indicating a limited influence on reservoir pore structure complexity. Feldspar is easily dissolved, creating dissolution pores. As the feldspar content increased, the dissolution pores also increased, enhancing pore connectivity and permeability, thereby reducing heterogeneity. However, dissolution pores facilitate the formation of clay minerals, which subsequently fill the pores and throats, thereby reducing pore space and increasing the structural complexity and heterogeneity. A higher carbonatite content promotes carbonate cementation, which reduces pore size, blocks the throat, and increases heterogeneity, resulting in a higher fractal dimension. In contrast, the chlorite content had a weak negative correlation with the fractal dimension (R² < 0.4). A higher chlorite content corresponds to a lower fractal dimension. Chlorite formation occupies the pore space, reducing the storage capacity and permeability. However, chlorite forms a cementing film on mineral particles, which inhibits compaction and helps preserve the pore structure, thereby reducing heterogeneity. Additionally, increased chlorite content creates uniform tiny pores that further lower the fractal dimension.

In summary, various mineral components substantially influence the complexity of the reservoir pore structure. The combined effects of these mineral components reflect the reservoir’s physical properties. In addition, changes in the mineral composition indicate reservoir connectivity, providing a foundation for heterogeneity assessments. Therefore, analyzing mineral content is essential for predicting pore structure, connectivity, and heterogeneity characteristics.

5.6. Geological Significance of D

The D_MIP revealed that the pore structure of tight sandstone reservoirs exhibits distinct dual-fractal properties, which expose its complexity and variability in multiscale space. D_MIP characterizes the connectivity of the three-dimensional pore-throat structure and the tortuosity of flow paths, thereby quantitatively characterizing reservoir heterogeneity. Integrating SEM imaging with mercury injection experiments enables the qualitative identification of pore morphology and quantitative extraction of structural parameters. Particularly, with the introduction of deep learning techniques, a large amount of pore information can be efficiently extracted from SEM images. Pore-type boundaries can be automatically recognized and classified. D_SEM quantifies the geometric complexity and morphological diversity of pore boundaries. D_MIP primarily characterizes the spatial connectivity and permeability of pores, whereas D_SEM captures the heterogeneity and complexity of pore morphology on a 2D plane. Combining both methods enables the characterization of the reservoir pore structure across multiple scales and enhances the understanding of fluid flow mechanisms and reservoir performance. This integrated approach provides technical support for the classification, evaluation, and development of tight sandstone reservoirs, as well as for rock physics modeling.

Furthermore, significant correlations were observed between the fractal dimension and pore structure parameters, geometric characteristics, and mineral composition. By thoroughly exploring these relationships, key factors influencing the pore structure can be identified and used to predict the heterogeneity of the reservoir and its evolution trend. The pore characteristics of tight sandstone are influenced by geological processes, including the sedimentary environment, diagenesis, and mineral composition. Sedimentation primarily affects the macroscopic characteristics of the pore structure. Dense sandstones typically consist of sand grains, with the pores between the grains forming a large-scale pore-throat system. The particle size and arrangement of the initial sediments determine these large pore-throats. Different sedimentary environments result in pore-throat systems of varying scales, with grain size distribution, particle shape, and deposition mode all influencing pore distribution characteristics. Diagenesis, through processes such as compaction, cementation, dissolution, and mineral precipitation, forms smaller-scale pore-throat systems. The Chang 8 reservoir is primarily composed of a grey sandstone and dark mudstone interbedded sequence, with the depositional environment being mainly underwater distributary channels and interdistributary bays, representing a typical shallow-water deltaic sedimentary system. The lithology is dominated by fine-grained feldspathic sandstone and feldspar-rich lithic sandstone, with complex detrital components, low compositional maturity, and low to moderate structural maturity. The burial depth is greater than 2200 m, and compaction reduces the original pore space of the reservoir. Cementation destroys some primary porosity and damages particular secondary dissolution pores, leading to a finer pore-throat structure. As a result, the reservoir pore structure is complex, and the fractal dimension is high. Therefore, in the future, performing fractal dimension calculations and spatial distribution analysis on wellbore profiles and regional planes will effectively reveal the mechanisms by which sedimentary-diagenetic processes influence pore structure evolution and reservoir quality.

Fractal-derived pore classifications can effectively guide reservoir management strategies. In Type I and Type II reservoirs, due to the higher porosity and the coexistence of large and small pore-throat systems, development should separately address the characteristics of both pore types. In regions with higher porosity, the focus should be on developing large pore-throats using conventional high-pressure fracturing techniques for extraction. In areas with lower porosity or where micropores dominate, techniques such as acidizing and micro-fracture formation should be used to enhance the extraction of micropores. A phased development strategy can also be employed: first, large pore-throat systems can be accessed through high-pressure, large-volume fracturing, followed by micro-fracturing or acid fracturing to enhance micropore connectivity, achieving more comprehensive reservoir development. Type III reservoirs, with poor permeability, are mainly composed of tiny pores. The pore-throat radius are small, the pore structure is simple, and the connectivity is poor, displaying clear monofractal characteristics. The development strategy for such reservoirs should focus on using small-volume, high-pressure fracturing techniques combined with acid fracturing technology for extraction. Small-volume, high-pressure fracturing can effectively prevent damage to the pore structure. In contrast, acid fracturing can dissolve carbonate minerals in the reservoir, improving micropore connectivity and the reservoir’s mining effect.

6. Conclusions

The complex pore structure of tight sandstone reservoirs poses significant challenges for their quantitative characterization. This study employed experimental tests, deep learning technology, and fractal geometry theory to quantitatively analyze the pore structure characteristics of Chang 8 tight sandstone in the Jiyuan area of the Ordos Basin and to further explore the factors affecting the fractal dimension. The main conclusions are as follows:

(1)

HPMI reveals the complex and highly heterogeneous nature of the pore structure in tight sandstone reservoirs, demonstrating distinct fractal segmentation. Fractal dimension correlates with reservoir quality. The D_MIP values for the Type I, II, and III reservoirs increased sequentially, indicating that as reservoir quality decreased, pore complexity and heterogeneity increased, and connectivity decreased. Additionally, the average fractal dimensions of the small and large pore-throats were 2.16 (D₁) and 2.52 (D₂), respectively, indicating greater complexity in large pore-throat structures.

(2)

The deep learning-based SEM pore extraction technique effectively quantified the pore structure of tight sandstone. Analysis of the fractal dimension and geometric parameters reveals the pore morphology and its microscopic complexity. The study found that the pore structure became more complex as the reservoir quality decreased, and the pore morphology became more irregular. Specifically, the D_SEM increased as the with the deterioration of reservoir quality. Type I reservoirs had the smallest fractal dimension, followed by Type II, with Type III showing the highest values. Additionally, reservoir quality exhibits strong correlations with pore geometric features; negative correlations with pore perimeter, aspect ratio, and solidity; and positive correlations with circularity and major axis length.

(3)

The fractal dimensions D_MIP and D_SEM of the studied reservoirs ranged from 2.21 to 2.49 and from 1.01 to 1.28, respectively. This difference may be due to the distinct theoretical principles and computational models underlying the two methods. D_MIP reflects changes in pore connectivity and permeability, whereas D_SEM focuses on pore morphology and microscopic geometric characteristics. Collectively, these two methods reveal the pore structure’s complexity and heterogeneity at different scales and characterize its multiple features.

(4)

A significant correlation exists between the fractal dimension of tight sandstone reservoirs and their structural characteristics, geometric shape parameters, and mineral composition. The fractal dimension demonstrates an inverse relationship with permeability, porosity, median radius, maximum mercury saturation, mercury withdrawal efficiency, and sorting factor, while showing a positive link with median pressure and displacement pressure. Among these, the maximum mercury saturation and sorting factor demonstrate a strong correlation with the fractal dimension (R² > 0.8). Additionally, the fractal dimension is negatively correlated with pore circularity and major axis length and positively correlated with perimeter, aspect ratio, and solidity. Pores with higher circularity and simpler structures correspond to lower fractal dimensions, whereas irregular and long-strip pores with complex structures and poor connectivity correspond to higher fractal dimensions. In terms of mineral composition, the fractal dimension has a negative association with the concentrations of feldspar, quartz, and chlorite, and a positive correlation with carbonate content.

(5)

The pore structure of dense sandstone reservoirs exhibits distinct dual-fractal characteristics, revealing its complexity and heterogeneity across multiple scales. Differences in the sedimentary environment and diagenesis jointly control the reservoir’s pore structure characteristics. Therefore, the reservoir management strategy must fully account for differences in pore types, especially in Type I and II reservoirs, where the dual-fractal characteristics of the pore structure significantly impact development design.