Fractal Characteristics of Pore Structure of Longmaxi Shales with Different Burial Depths in Southern Sichuan and Its Geological Significance

Abstract

Burial depth can significantly impact the pore structure characteristics of shale. The Lower Silurian Longmaxi Shale in the Weiyuan block of the Sichuan Basin is a marine formation that we studied for deep shale gas exploration. We used two groups of Longmaxi samples, outcrop shale and middle-deep shale, to investigate the pore structure fractal features at varying burial depths using a combination of mineralogy, organic geochemistry, scanning electron microscopy (SEM), and low-temperature gas (CO₂, N₂) adsorption. The V-S fractal model was used to determine the fractal dimension (Dc) of micropores, and the FHH fractal model was used to determine the fractal dimension (D_N) of mesopores. The findings indicate that the pore morphology of organic matter becomes irregular and more broken as the burial depth increases, as does the content and maturity of organic matter. The pore size of organic matter gradually decreases, the SSA (BET, DR) and PV (BJH, DA) of shale pores increase, the pore structure becomes more complex, and the average shale pore size decreases. According to this study, the organic matter content and its maturity show an increasing trend as burial depth increases. Meanwhile, the organic matter’s pore morphology tends to be irregular, and fracture rates rise, which causes the organic matter’s pore size to gradually decrease. In addition, the SSA (comprising the values assessed by BET and DR techniques) and PV (evaluated by BJH and DA methods) of shale pores grew, suggesting that the pore structure became more complex. Correspondingly, the average pore size of the shale decreased. The fractal dimensions of the micropores (D_C), mesoporous surface (D_N1), and mesoporous structure (D_N2) of outcrop shale are 2.6728~2.7245, 2.5612~2.5838, and 2.7911~2.8042, respectively. The mean values are 2.6987, 2.5725, and 2.7977, respectively. The D_C, D_N1, and D_N2 of middle-deep shale are 2.6221~2.7510, 2.6085~2.6390, and 2.8140~2.8357, respectively, and the mean values are 2.7050, 2.6243, and 2.8277, respectively. As the fractal dimension grows, the shale’s pore structure becomes more intricate, and the heterogeneity increases as the buried depth increases. The fractal dimension has a positive association with the pore structure parameters (SSA, PV), TOC, and R_o and a negative association with the mineral component (quartz, feldspar, clay mineral) contents. Minerals like quartz, feldspar, and clay will slow down the expansion of pores, but when SSA and PV increase, the pore heterogeneity will be greater and the pore structure more complex.

1. Introduction

Shale gas is a special kind of natural gas that can produce and store energy on its own [1]. Thanks to developments in geological theory and shale gas exploration technology, China’s shale gas production has increased dramatically in recent years. The Lower Paleozoic Wufeng-Longmaxi Formation in the Sichuan Basin and its surrounding areas is the primary target for shale gas development in China. Shale gas demonstration zones have been constructed at the state level, including Jiaoshiba, Weiyuan, and Changning-Zhaotong [2]. Reservoirs of deep shale have been found that are more than 3500 m below the surface. With their substantial oil and gas potential, deep shale reservoirs will progressively become more relevant in the subsequent exploration phase. The deep shale reservoirs differ from the shallow ones in that they are buried deeper, are exposed to more extreme temperatures and pressures, and have a higher degree of densification [3]. Comparing the pore structure characteristics of shale reservoirs with different burial depths is essential for promoting the development of deep shale gas.

A variety of pore categorization methods have been established based on pore size, pore matrix, pore morphology, and pore connectivity [4,5,6,7]. The International Union of Pure and Applied Chemistry (IUPAC) proposed a pore classification standard, which is now extensively used in the quantitative description of shale pore. IUPAC separates pores into the following three categories: Micropores (less than 2 nm), mesopores (between 2 nm and 50 nm), and macropores (more than 50 nm). According to Bu et al., mesopores or micropores offer more surface area and adsorption energy for adsorbed gas, whereas macropores offer room for free gas [8]. The storage capacity, desorption difficulties, and seepage characteristics of shale gas are directly determined by the pore structure characteristics of shales. These factors also impact the gas content, reserve estimate, and development appraisal of shales [9].

The two methods currently being studied regarding the nanopore structure of shale are high-resolution imaging technology and fluid/non-fluid injection technology. The development of field emission scanning electron microscopy (FESEM), focused ion beam scanning electron microscopy (FIBSEM), focused ion beam helium ion microscopy (FIBHIM), and transmission electron microscopy (TEM) has greatly promoted the intuitive and qualitative observation of shale’s organic, mineral structure and pore fissure structure, and has continuously deepened the study of ultra-structural morphology and the genesis of oil and gas reservoirs [10,11]. Furthermore, pore size distribution (PSD), specific surface area (SSA), pore volume (PV), porosity, and other parameters are frequently obtained through the use of nuclear magnetic resonance (NMR), mercury intrusion porosimetry (MIP), gas (N₂ and CO₂) adsorption (GA), and other experiments for the quantitative analysis of shale pore structure [12,13,14]. Therefore, the investigation of shale pore structure using a variety of experimental techniques has grown significantly in recent years.

Pore geometry with uneven surfaces and shapes may be well described by fractal theory. The pore structure of the marine shale of Changning, southern Sichuan’s Longmaxi Formation, was examined by Li et al. using the FHH model [15]. Also using the FHH model, Li et al. performed a more thorough fractal and pore structure investigation of the deep shale of the Wufeng Formation-Longmaxi Formation [16]. Using a variety of fractal techniques, Ma et al. conducted a fractal analysis and investigated the pore structure of lacustrine shale in China’s Kongdian Formation [17]. Three types of study are now being conducted on the fractal dimension of shale: the FHH model, the BET model, and the thermodynamic model. The most popular approach and the best fit for shale reservoirs is the fractal FHH model [18].

The outcrop and the core (middle-deep) shale of Wei X well of Longmaxi Formation in southern Sichuan were selected as the research materials, and the shale petrology, mineralogy, organic geochemistry, and other aspects were studied. The pore structure of shale with varying burial depths was thoroughly described from both qualitative and quantitative perspectives using SEM, GA, and other testing methods. Based on this, an appropriate fractal model was chosen to examine the shale pores at various scales. Ultimately, a relationship was found between the fractal dimension, mineral composition, organic matter content, organic matter maturity, and shale pore structure characteristics. By comparing the pore structure features of shales with varying burial depths, this study aimed to investigate the resource potential of deep shale reservoirs using the shale in the Weiyuan block as an example.

2. Geological Setting

The Weiyuan block, with an area of around 6500 km², is situated south of the Sichuan Basin. The tectonic position in the southwestern Sichuan paleo-central slope of the low-folded zone and the development of the Weiyuan dorsal tectonics, Triassic System, and Jurassic System are exposed, with a longitudinal lack of the Devonian and Carboniferous Systems. In the northwestern part of the dorsal tectonics, rock layers of the Zhiru System are lacking to varying degrees [19]. The Chuanzhong Palaeouplift, Qianzhong Palaeouplift, and Yichang Underwater Uplift surround the research region, which was in a stagnant semi-deepwater-deepwater shelf depositional environment throughout the Late Ordovician to Early Silurian. Black shales that were heavily bedded (10~30 m thick), high-maturity (R_o > 2%), rich in organic matter (TOC > 2 wt.%), and very brittle were deposited. The depth of the Wufeng-Longmaxi Formation’s shales in the Weiyuan area ranges from 1500 to 4000 m, and they progressively deepen from north to south in an easterly direction due to the influence of several tectonic movements in the later stages, including the Caledonian, Hercynian, Indo-Chinese, Yanshanian, and Himalayan periods [20]. The most advantageous shale gas exploration and production system in the Sichuan Basin is the Longmaxi Formation, which produces siliceous, carbonaceous, calcareous, and clayey shale from bottom to top, locally intermingled with black siltstone shale [21].

3. Samples and Experiments

3.1. Samples

The 20 shale samples utilized came from the Lower Silurian Longmaxi Formation in the Weiyuan block, southern Sichuan. Three samples were taken from the measured profile of the field outcrops; six samples were taken from the middle shale formation, with sampling depths ranging from 2651.09 to 2943.8 m; and 11 samples were taken from the deep shale formation, with sampling depths ranging from 3552.58 to 3574.54 m. Seventeen middle and deep shale samples came from the same locations and wells as the samples that were characterized extensively in previous work (data from Hao et al., 2023) [22]. The 20 collected samples were examined for TOC, R_o, XRD analysis, and SEM observation. Six of them were tested for GA.

3.2. Experiments

The LECO CS-230 carbon-sulfur analyzer was used to determine TOC. The materials were crushed to 200 mesh prior to the experiment, and the inorganic carbon was eliminated by adding a diluted hydrochloric acid. The samples were then neutralized with distilled water and dried. TOC was ascertained in the experiment after 1.0 g of iron flux and 1.0 g of tungsten flux were applied to the dried samples. A Japanese Rigaku TTR III multifunctional X-ray diffractometer was used for XRD investigations. A suitable powder sample was evaluated during the test and analysis using the following parameters: tube voltage of 35 kV, tube current of 30 mA, scanning range of 2θ = 5~80°, and scanning speed of 2°/min. By examining the XRD pattern features and diffraction peak strength of distinct mineral crystals, the content of different minerals in the sample was ascertained. The pore morphology of the shale samples was characterized using a Zeiss Sigma 500 SEM. Before the test, the samples were processed into cubes about 1 cm in size. Subsequently, the samples were dried in an oven. A flat and smooth surface was selected and tested after gold plating on the smooth surface. During the test, the secondary electron resolution reached 1 nm, the magnification was 200,000 to 800,000 times, and the acceleration voltage adjustment range was 0.02–30 kV. The ASAP 2460 surface area and porosity analyzer was used for GA experiments. Prior to the experiment, the samples were crushed to 200 meshes. In order to eliminate moisture and volatile materials from the sample, it was initially placed in a degassing station and allowed to degas at 110 °C for 10 h. The degassed samples were then transferred to the analysis station, where high quality N₂ (purity > 99.9%) was used as the adsorbate for the adsorption tests, which were conducted at 77.35 K. The sample pretreatments for the CO₂ adsorption experiments were similar to those of the N₂ adsorption experiments. The CO₂ adsorption curves were obtained at 273 K after the powder samples were degassed for 12 h. The CO₂ was used to characterize the pore information of micropores and N₂ was used to identify the pore information of mesopores. The DR and BET models were used to calculate the SSA of shale pores. The DA and BJH models were used to determine PV and PSD.

3.3. Fractal Theory

The fractal dimension of the micropores was calculated using the fractal V-S model based on CO₂ adsorption measurements, and the formula was [23,24]:

(1)$\ln \left(V\right)={\displaystyle \frac{3}{D_C}}\ln S+\mathrm{C}$

In the equation: V—gas adsorption volume cm³/g; S—pore cumulative specific surface area m²/g; D_c—microporous fractal dimension; C—constant;

Shale fractal dimension was calculated using the fractal FHH model based on N₂ adsorption tests [18,25] and the formula was [26]:

(2)$\ln \left(V\right)=\left(D_N-3\right)\times \ln \left(\ln {\displaystyle \frac{P_0}{P}}\right)+\mathrm{C}$

In the equation: V—Adsorption gas volume at varying relative pressures, cm³/g; P—equilibrium pressure, MPa; P₀—Adsorbed gas saturation vapor pressure, MPa; C—constant; D_N—fractal dimension of the porous materials.

The range of the fractal dimension (D) is two to three. Three denotes very complicated surfaces or uneven pore structure, and two denotes flawlessly regular smooth solid surfaces or homogenous pore structure.

4. Results

4.1. Organic Geochemistry and Mineralogy

The TOC values range from 1.67 wt.% to 6.36 wt.%, with an average of 3.471 wt.%, indicating that the shales have favorable conditions for gas production, demonstrating good potential for hydrocarbon production. The TOC values of outcrop and middle-deep shale are 1.67 wt.%~1.94 wt.% and 2.24 wt.%~6.36 wt.%, respectively, and the average values are 1.79 wt.% and 3.77 wt.%, respectively [22]. It was discovered that middle-deep shale has a greater TOC value than outcrop. This shows that as burial depth increases, the TOC values progressively increase as well.

The degree of organic matter conversion to hydrocarbons is directly reflected in the maturity of organic matter, making it a crucial indicator of shale hydrocarbon generation potential. The maturity of organic matter is generally reflected by the R_o. However, there is a lack of vitrinite in Longmaxi shales, so the asphaltene reflectance (R_b) is measured in this experiment. The empirical formula R_o = 0.618 × R_b + 0.4, presented by Jacob et al. in 1985, was used to obtain the R_o value [27]. The outcrop shales’ R_o fell within the high maturation stage, ranging from 1.78% to 1.80%, with an average of 1.795%. Meanwhile, the R_o of the middle-deep shales ranges from 2.032% to 2.26%, with an average of 2.143%, which belongs to the over-mature stage. The middle-deep shales, on the other hand, have an R_o that falls into the over-mature stage and varies from 2.032% to 2.26%, with an average of 2.143%. The high to over-mature state that the shales are now in provides a solid basis upon which the shale reservoir’s pore structure can develop. As a consequence, it is also found that as burial depth grows, so does the shale’s organic matter maturity.

Silica, carbonate, and clay minerals constitute the majority of the mineral makeup of the shales (Figure 1A). Siliceous minerals are dominated by quartz, with contents ranging from 23.5% to 52%, with an average of 35.82%. The feldspar contents range from 1.3% to 10.4%, with an average of 5.755%. Calcite and dolomite make up the majority of carbonate minerals. No carbonate minerals are detected in the outcrop shales. The carbonate contents of the middle-deep shales range from 10.9% to 52.1%, with an average of 30.94%. The clay mineral contents range from 15.6% to 48.3%, with an average of 29.29%. Illite predominates among the clay minerals. The contents of illite, I/S mixed layer, and chlorite are 49~83%, 4~37%, and 5~22%, respectively, and the average values are 66.6%, 19.7%, and 13.7%, respectively. (Figure 1B). The clay composition is dominated by illite, suggesting that the shales are at a high late diagenetic stage [28].

4.2. Pore Types in Shale at Different Burial Depths

Organic pores, inorganic pores (intercrystalline pores, intracrystalline-dissolved pores, clay mineral interlayer pores), and microfractures represent several categories of pores that can be distinguished by the SEM (Figure 2). The middle-deep shale has well-developed organic pores. In the deep shale, the morphology of organic pores is distributed heterogeneously. Most of them are honeycomb, elliptical, and irregular. Some of the morphologies are more ruptured. The pore size is below 500 nm (Figure 2A). This could have something to do with the high gas production during the thermal development of maturation and the collapse and carbonation of the organic pore skeleton following the over-maturing of the deep shale [28]. The morphology of organic pores in the middle shale is comparatively homogeneous. They are mainly circular organic pores and have large pore sizes, mainly concentrated below 2 μm (Figure 2B). As burial depth increases, the organic pore size is increasingly smaller. The formation of organic pores is not observed in outcrop shales. It could be because the outcrop shales have experienced a range of geologic processes over the course of their geologic history, such as compaction, diagenesis, and weathering. The growth and production of organic matter pores may be impacted by these processes. Furthermore, one of the main reasons limiting the formation of organic matter pores is exposure to the environment. The outcrop shale is exposed to the surface and is affected by weathering, erosion, and other environmental elements, which may also destroy the original pore structure and make it difficult to preserve organic pores.

The bulk of crystalline pyrite (Figure 2B,C,E,F), which is produced in anoxic environments, is found in middle-deep shales and outcrops. Crystalline pyrite comprises a high number of pyrite crystals with uniform cubic grains. The shape of intergranular pores developed between pyrite is mostly irregular. The pore size ranges from tens of nanometers to hundreds of nanometers. The type of pores is usually isolated in the shale matrix. Gas seepage is hampered by the inadequate connection between these pores [4]. Crystalline pyrite is mostly seen in deep shales in association with organic matter, forming organic pores within the organic matter (Figure 2E). These organic pores adsorbed on pyrite particles have some ability to adsorb natural gas and are a very important pore type in shales [29].

Intracrystalline solution pores form in the middle-deep shales, especially in carbonate minerals like calcite and dolomite. Most of the pores have irregular shapes, such as oval, elongated, and triangular (Figure 2F,I). This phenomenon may occur because of the release of organic acids during the decomposition of organic matter. These organic acids can dissolve carbonate minerals in large quantities, resulting in the formation of dissolution pores, and the pore size of these pores is often less than 1 μm. Most of these pores are relatively isolated with poor connectivity, making little contribution to shale gas seepage [28].

The primary constituents of clay minerals are illite and I/S mixed layer. Numerous interlayer pores of clay minerals develop in both the outcrop and the middle-deep shales. Illite is in the form of thin lamellae with distinct slit-shaped pores developed between the lamellae (Figure 2A,F,G) and pore sizes below 500 nm. During sedimentary burial, montmorillonite transforms into I/S mixed layer and illite, resulting in pores created by volume reduction. These interlayer pores can serve as tiny transport channels for shale gas seepage since they are somewhat connected to one another.

As microfractures grow, they can store free gas and aid in the desorption of adsorbed gas, which is a crucial channel for gas seepage in shales [30]. Microfractures mainly develop at the edges of clay minerals in outcrops and middle-deep shales. They are jagged and curved, with large extension lengths. The width of microfractures reaches the nanometer scale (Figure 2A,H,I). The generation of these microfractures may be related to post-generation modification effects such as tectonic movements, shale reservoir fracturing effects, and differential horizontal compaction [29]. Microfractures may provide important gas storage space and promote the extension of fracture-induced fractures in the later stages of fracturing.

4.3. Pore Structure

4.3.1. CO₂ Isothermal Adsorption Curve

The CO₂ adsorption curve type aligns with the IUPAC-defined type I isotherm (Figure 3A) [31]. The shale exhibits micropore-filling properties, suggesting that it has a certain number of micropores [32]. The CO₂ adsorption curves for shallow–middle–deep samples are similar. The adsorption volume also exhibited a rising trend when the relative pressure increased in the region of P/P₀ < 0.035. However, there are differences in the maximum adsorption volume. The outcrop samples have the smallest adsorption volume., which is 1.2158 cm³/g~1.2320 cm³/g. The middle–deep samples have a higher adsorption volume than the outcrop samples, which is 1.8041 cm³/g~2.4985 cm³/g. This demonstrates that the microporous pore structure of shale samples varies depending on their depth.

DR and DA models were used to determine the SSA and PV of shale micropores at different depths (Table 1). The SSA of outcrop and middle–deep shale micropores ranges from 9.4408 to 9.8153 m²/g and 14.124 to 20.7664 m²/g, with mean values of 9.6281 m²/g and 16.9684 m²/g, respectively. The PV ranges from 0.0051 to 0.0052 cm³/g and 0.0068 to 0.0094 cm³/g, with mean values of 0.0052 cm³/g and 0.0079 cm³/g, respectively. The SSA and PV of shale micropores increase with increasing burial depth, which further indicates that the number of micropores rises and the pore structure becomes increasingly complicated.

The PSD of shale micropores is described using the DA model. The PSD peaks of O1, O2, M1, M5, D1, and D11 are 1.5125 nm, 1.5227 nm, 1.4857 nm, 1.5045 nm, 1.4662 nm, and 1.4948 nm, respectively (Figure 3B). The pore sizes of outcrop and middle–deep shale are concentrated at 1.5125~1.5227 nm and 1.5125~1.5227 nm, respectively. According to Table 1, the average pore diameters of outcrops and middle–deep samples are 1.7056~1.7149 nm and 1.6306~1.6903 nm, respectively, and the average values are 1.7103 nm and 1.6628 nm, respectively. Regardless of the PSD or average pore size, the outcrop shale has a larger pore size than the middle–deep shale. This might be because the deep shale has a higher formation pressure.

4.3.2. N₂ Isothermal Adsorption Curve

Overall, the isothermal adsorption curves of the shallow–middle–deep shale samples primarily exhibit an inverse S shape, according to the results of the N₂ adsorption–desorption curves (Figure 4). The isothermal adsorption curves are classified as type IV in accordance with the IUPAC classification scheme for isothermal adsorption curves [31], and the hysteresis loops are comparable to type H3, indicating that the pores in the shales are mesopores originating from slits.

Three phases may be distinguished in the adsorption process based on the trend of the N₂ adsorption curve: (1) The adsorption curve climbs gradually and has a short slope when the relative pressure (P/P₀) is less than 0.45. The presence of micropores is shown by the adsorption volume not being 0 when the relative pressure (P/P₀) is 0; (2) The capillary condensation phenomenon causes a hysteresis loop to emerge between the adsorption-desorption curves when the relative pressure (P/P₀) is between 0.45 and 0.9. The hysteresis loop of the middle–deep sample is larger than that of the outcrop. The larger the hysteresis loop, the greater the number of mesopores, meaning that there are more mesopores in the middle–deep sample; (3) The adsorption curve steepens quickly when the relative pressure (P/P₀) is between 0.9 and 1, and it does not attain adsorption saturation when the relative pressure is approximately equal to 1. The cause is gas condensation, which shows that there are some macropores or microcracks in the shale. The adsorption volume of middle–deep shales is greater than that of outcrop shales when the adsorption volumes of shales with varying burial depths are compared. This suggests that the middle–deep shales contain more pores and more intricate pore structures.

The SSA and PV of mesopores are calculated using the BET and BJH models, respectively. Table 1 displays the specifics. The SSA of the outcrops and middle–deep shale mesopores are 8.8087~11.3879 m²/g and 21.2077~29.3799 m²/g, with mean values of 10.0983 m²/g and 23.9183 m²/g, respectively. The PV is 0.0092~0.0117 cm³/g and 0.0185~0.0260 cm³/g, with mean values of 0.0104 cm³/g and 0.0220 cm³/g, respectively. According to the aforementioned investigation, the middle–deep shale’s SSA and PV are greater than those of the outcrop shale. This indicates that the middle–deep shale’s pores are more developed and have a more complex pore structure.

The PSDs of shale mesoporous were analyzed in conjunction with BJH theory. As shown in Figure 5, the samples O1, O2, M1, M5, D1, and D11 all have two peaks, which are 2.46 nm and 29.82 nm, 2.86 nm and 7.84 nm, 2.65 nm and 20.87 nm, 2.66 nm and 21.58 nm, 2.86 nm and 12.54 nm, and 2.65 nm and 15.62 nm, respectively. This shows that the probability of aperture appearing at this peak is the highest. The average pore sizes of the outcrop and middle–deep samples are 5.6448~7.6146 nm and 5.0852~5.6811 nm, respectively, and the mean values are 6.6297 nm and 5.4336 nm, respectively (Table 1). The outcrop shale has greater average pore sizes than the middle and deep shale. This is because, after the shale is deposited, the pressure of the layers above it rises as the buried depth increases, improving compaction. This compaction will compress the pores and decrease their size in the middle–deep shale. The compaction of outcrop shale is relatively weak, so the pores can maintain a relatively large pore size to a certain extent. Stronger heterogeneity and a more complicated pore structure are found in shale with lower pore sizes.

4.3.3. Fractal Characteristics

The fractal dimension (D_C) of the micropores was determined using the fractal V-S model based on CO₂ adsorption tests. Figure 6 displays the fractal fitting findings. With an average value of 2.7029 and a correlation coefficient (R²) more than 0.99, the D_C of the shale micropores at various depths varies from 2.6221 to 2.7510. The highly complex and diverse pore structure of micropores is indicated by the fractal dimension being near 3. The D_C of outcrop and middle–deep shale are 2.6728~2.7245 and 2.6221~2.7510, respectively, and the average values are 2.6987 and 2.7050, respectively. As shale burial depth increases, the pore structure becomes more complex and varied. A higher percentage of adsorbed gas content is seen in shale with larger fractal dimensions because the more micropores develop, the more gas adsorption sites and adsorption potentials are available.

A fractal FHH model derived from N₂ adsorption studies was used to determine the fractal dimension (D_N) of the mesopores. Because of the hysteresis phenomenon, the adsorption and desorption curves do not overlap at a relative pressure of 0.45, indicating that the pore structure is significantly changed before and after this relative pressure. The fractal dimension of shale is determined by linearly fitting the adsorption curves with P/P₀ = 0.45 as the cut-off line, as seen in Figure 7. Double fractals are discovered to be a characteristic of shale pores. The D_N1 (P/P₀ < 0.45) mainly reflects the monomolecular-multimolecular adsorption and filling occurring within the micropores and can characterize the irregularity and complexity of the pore surface. The D_N2 (P/P₀ > 0.45) usually characterizes the complexity and irregularity of the interior space of the pores, mainly reflecting the capillary cohesion.

Fractal fitting results are shown in Figure 7. D_N1 and D_N2 are 2.5612~2.6390 and 2.7911~2.8357, respectively, and the mean values are 2.6070 and 2.8177, respectively. Both D_N1 and D_N2 are close to 3, but D_N2 is larger than D_N1, demonstrating that the inside structure of the pore is more complicated than the surface. The D_N1 of outcrop and middle–deep shale are 2.5612~2.5838 and 2.6085~2.6390, respectively, and the average values are 2.5725 and 2.6243, respectively. D_N2 are 2.7911~2.8042 and 2.8140~2.8357, respectively, and the mean values are 2.7977 and 2.8277, respectively. When shale is exposed to the surface, its fractal dimension is at a low level, and the pore structure is relatively simple. However, with the deepening of burial depth, the fractal dimension progressively grows, the pore structure of the shale becomes more intricate, and the heterogeneity is significantly enhanced.

5. Discussion

5.1. Effect of Pore Structure on Fractal Dimension

The intricacy of shale pore structure may be quantitatively described by the fractal dimension, which also reveals the shale pores’ potential for gas adsorption. In general, the more complex the pores and the greater the gas adsorption capacity, the bigger the fractal dimension [33]. It was demonstrated that the adsorbed gas content of shale is controlled by SSA, whereas the free gas content is controlled by the PV. The majority of PV is contributed by micropores and mesopores. Micropores contribute significantly more to shale’s SSA. Typically, micropores account for less than 20% of PV. Nonetheless, over 80% of SSA may be supplied by micropores [34].

The fractal dimension has a strong positive link with both SSA and PV (Figure 8). This finding is in line with Zhao et al.’s research, which found a favorable correlation between fractal dimension and shale’s pore structure [35]. The correlation coefficient between D_C and (DR) SSA is 0.5976, and the correlation coefficients between D_N1 and D_N2 and (BET) SSA are 0.9159 and 0.7638, respectively (Figure 8A). The correlation coefficient between D_C and (DA) PV is 0.6063, and the correlation coefficients between D_N1 and D_N2 and (BJH) PV are 0.7833 and 0.7364, respectively (Figure 8B). The fractal dimension rises as SSA and PV grow, according to the research above. This demonstrates that the more developed shale micropores and mesopores are, the greater the heterogeneity, the more complex the pores, and the higher the PV and SSA.

5.2. Effect of TOC Content and R_o on Fractal Dimension

The content and thermal evolution degree of organic matter, a crucial carrier for the production of organic pores, influence not only the pore shape of organic matter but also the distribution of pore sizes, which in turn influences the fractal dimension. The analysis focuses on the relationships between D_C, D_N1, D_N2, and TOC. The findings demonstrate a positive relationship between TOC and D_C, D_N1, and D_N2 (Figure 9A), with correlation coefficients of 0.4932, 0.7646, and 0.4871, respectively. This suggests that as TOC rises, so does the complexity of the shale pore structure and its adsorption capacity. Thus, it can be concluded that more organic micropores and mesopores form during the pyrolysis process as TOC rises. Additionally, the higher SSA and rougher surfaces of these pores contribute to their heterogeneity and complex pore structure. As shale’s pore structure becomes more complex, its fractal dimension grows, giving gas molecules more adsorption sites and enhancing its storage capacity.

The morphology and level of development of organic pores in shales are directly linked to the stage of hydrocarbon evolution. The morphology, pore size, and development degree of the organic pores have obvious differences at different stages of thermal evolution. Therefore, the degree of thermal development experienced by organic matter will also become an essential component impacting the change of the fractal dimension of shale. The degree of thermal evolution and D_C, D_N1, and D_N2 are shown to be positively correlated, according to an analysis of the relationship between R_o and fractal dimension (Figure 9B), with correlation coefficients of 0.3843, 0.7633, and 0.7171, respectively. As organic matter reaches the high maturity stage, its ability to produce hydrocarbons increases. Additionally, the organic pores have a simple pore structure and are primarily round and oval in shape. The aromatization of organic matter intensifies in the overmature stage as maturity increases. Additionally, the pore’s inner wall gets rougher, and it also reduces the support capacity of the pore. The pore becomes distorted, its connection decreases, its structure becomes complex, and its fractal dimension increases when subjected to the pressure of the rock layer above it [28].

5.3. Effect of Mineral Composition on Fractal Dimension

The degree of pores development is directly linked to the magnitude of the fractal dimension. Thus, the fractal dimension is affected by a number of factors governing shale pores. Shale mineral composition, TOC, degree of thermal evolution, burial depth, and stage of diagenetic development are the primary contributing factors. The diagenetic minerals, as the direct carriers of inorganic pore development, control the development of inorganic pores. This paper mainly analyzes the correlation between fractal dimension and mineral compositions such as quartz, feldspar, and clay minerals (Figure 10). The findings indicate that there is no relationship between quartz content and D_C. There is a weak negative correlation between D_N1 and D_N2 and the amount of quartz; their respective correlation coefficients are 0.1342 and 0.4385 (Figure 10A). There is a strong negative correlation between D_C, D_N1, and D_N2 and the amount of feldspar; their respective correlation coefficients are 0.6112, 0.6102, and 0.7818 (Figure 10B). Additionally, D_C, D_N1, and D_N2 exhibit a strong negative correlation with clay mineral content; their respective correlation coefficients are 0.4334, 0.8763, and 0.7952 (Figure 10C).

D_N1 and D_N2 have a weakly negative correlation with quartz content but no correlation with D_C (Figure 10A). The fractal dimension of mesopores decreases with increasing quartz content, indicating a more homogeneous pore structure with less heterogeneity. The crystalline structure of quartz is often uniform. The fractal dimension of the pore structure is reduced because the pore scale is primarily macropores, and the pores are comparatively more homogeneous [36]. Some researchers have discovered a negative correlation between fractal dimension and quartz content when it comes to the impact of quartz on shale pore development [36,37], which is in line with the findings of this investigation.

As aluminosilicate, feldspar is easily dissolved by fluids under buried conditions. In a buried environment, feldspar, an aluminosilicate mineral, is vulnerable to fluid erosion. As a result, feldspar readily develops into mesopores with enormous pore sizes and macropores when formation fluid dissolution is present. Wang et al.’s research revealed that with the increase of feldspar content, the fractal dimension gradually rose, which reflected the shale pore structure’s growing complexity. They hypothesized that this may be the result of many dissolving pores in feldspar forming later on [38]. On the opposite hand, this study’s D_C, D_N1, and D_N2 exhibit a strong negative association with its feldspar content (Figure 10B). It is hypothesized that this may be due to the strong brittleness of feldspar. Under the formation conditions, cleavage fractures are developed. The feldspar content and D_C, D_N1, and D_N2 are negatively correlated as a result of this portion of the cleavage fractures increasing the equivalent pore width [35].

The formation of shale pores is significantly influenced by clay minerals, one of the major inorganic minerals [39,40]. According to the correlation study, there is a negative link between the clay mineral content and D_C, D_N1, and D_N2 (Figure 10C). The high amount of clay minerals, their small mineral particles, and their poor compaction resistance are thought to be the possible causes. The clay mineral particles tend to align during long-term compaction diagenesis, which reduces pore space and results in a simple pore shape [16,35].

In clay minerals, illite, I/S mixed layer, and chlorite are formed. As a result, the relationship between fractal dimension and illite, I/S mixed layer, and chlorite content will be analyzed (Figure 11). These findings indicate a negative association between illite content and D_C, D_N1, and D_N2, with corresponding correlation values of 0.4352, 0.4522, and 0.2187 (Figure 11A). The content of the I/S mixed layer has a positive association with D_C, D_N1, and D_N2, with corresponding correlation values of 0.6759, 0.8136, and 0.5168 (Figure 11B). D_C, D_N1, and D_N2 have a negative association with the chlorite content; the correlation coefficients are 0.2244, 0.5764, and 0.5499 (Figure 11C). As the amount of illite and chlorite in shale increases, its fractal dimension drops and its pore structure becomes more uniform, consistent with the correlation between fractal dimension and clay mineral content. As a result, clay minerals are influenced by illite and chlorite. The I/S mixed layer, on the other hand, has a positive association with the fractal dimension. This might be due to the incomplete conversion of montmorillonite into illite, and some montmorillonite influences the shale’s pore structure. When Nie et al. studied the marine-continental transitional coal-bearing shale, they also looked at the connection between the fractal dimension and the amount of the three clay minerals mentioned above [35]. The findings indicate that there is no association between chlorite and the fractal dimension, but illite and the I/S mixed layer have a positive correlation with the fractal dimension. Different from the relationship between illite, chlorite, and fractal dimension in this study, it is speculated that it may be due to the different research objects. Marine shale is used in this study, and marine-continental transitional shale is the research object.

5.4. Effect of Burial Depth on Fractal Dimension and Geologic Significance

The fractal dimension of shale is significantly influenced by burial depth. The shale in the outcrop has a small fractal dimension and a very simple pore structure. The fractal dimension and the complexity of the pore structure increase as the burial depth increases because the middle–deep shale experiences stronger compaction, the pore diameter decreases, the heterogeneity is improved, and the pore surface becomes rougher.

The temperature and overburden pressure of shale will rise in proportion to the burial depth. There is a positive correlation between burial depth and shale’s fractal dimension. On the one hand, the shale organic matter moves into the high-over mature stage as the burial depth increases and the earth’s temperature rises. The number of irregular organic pores is significantly increased by the high hydrocarbon production of organic matter. However, as compaction is increased, the shale’s pore structure is crushed and distorted, increasing the pore structure’s complexity and fractal dimension.

With a high degree of thermal evolution and a high organic matter content, the Longmaxi shales in the Weiyuan Block in south Sichuan provide a solid basis for shale gas development. Furthermore, the middle–deep Longmaxi shales in southern Sichuan include well-developed organic pores, including micropores and mesopores, which have the capacity to produce source-generation and source-reservoirs on a small scale.

6. Conclusions

(1) Longmaxi shales have an average TOC of 3.471 wt.%, with values ranging from 1.67 wt.% to 6.36 wt.%. The phase of organic matter maturity is high to over-mature. The deeper the burial, the higher the organic matter content and maturity. Silica, carbonate, and clay minerals make up the majority of the minerals found in shale.

(2) The morphology of organic matter pores gradually becomes irregular and tends to break as the burial depth increases, and the pore size likewise decreases accordingly. In the shale samples, it can be observed that intergranular pores of pyrite, interlayer pores of clay minerals, and tiny cracks have developed. Furthermore, with the increase in burial depth, both SSA (measured by BET and DR methods) and PV (measured by BJH and DA methods) show an increasing trend, making the pore structure more complex. At the same time, as burial depth increases, the average shale pore size steadily decreases.

(3) In comparison with the outcrop shale, the middle–deep shale has greater fractal dimensions D_C, D_N1, and D_N2, suggesting a more complex pore structure and more heterogeneity as the buried depth increases. D_C, D_N1, and D_N2 have a positive correlation with the pore structure parameters, TOC and R_o, and a negative correlation with the mineral composition. The more complicated the pore structure, the stronger the pore heterogeneity becomes as SSA and PV rise. Minerals like quartz, feldspar, and clay will slow down the formation of nanopores.

(4) The middle–deep shales are subjected to stronger compaction as the burial depth increases. The pores become smaller, and the heterogeneity is enhanced. Consequently, the fractal dimension and the pore structure’s complexity both rise. A reference for estimating the resource potential of deep shale reservoirs in the Weiyuan block is supplied through a comparison of the pore structure and fractal features of shale at various depths, which reveals that the burial depth considerably impacts the fractal dimension of shale.

Author Contributions

Conceptualization, M.Y. and Y.P.; methodology, H.F.; software, Y.P.; validation, Y.L., W.W. and Y.Q.; formal analysis, Y.P.; investigation, H.F.; resources, H.Z.; data curation, Y.P.; writing—original draft preparation, M.Y. and Y.P.; writing—review and editing, Y.P., Q.Y. and H.Z.; visualization, H.F.; supervision, Y.P.; project administration, H.F.; funding acquisition, H.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. Mineral composition (A) and the relative contents of clay mineral (B). Data from Hao et al. [22].

Figure 2. SEM images of Longmaxi shales at different burial depths. (A): Sample D10, organic pores, clay mineral interlayer pores, microcracks; (B): Sample M1, organic pores; (C): Sample O1, intergranular pores; (D): Sample D5, intergranular pores; (E): Sample D7, intergranular pores; (F): Sample M1, clay mineral interlaminar pores, calcite intergranular dissolution pores; (G): Sample O1, clay mineral interlaminar pores; (H): Sample O1, microcracks; (I): Sample M2, dolomite intergranular dissolution pores, microcracks.

Figure 3. CO2 adsorption curves (A) and PSD (B) of samples based on CO2 adsorption experiments.

Figure 4. N2 adsorption curves of shale with different burial depths. Note: The blue dotted line represents a relative pressure of 0.45.

Figure 5. Pore size distribution curve of shale based on N2 adsorption experiments.

Figure 6. Shale pore fractal fitting curves based on CO2 adsorption experiments.

Figure 7. Shale pore fractal fitting curves based on N2 adsorption experiments. Note: Green represents the fractal dimension DN1 of relative pressure [less than] 0.45; red represents the fractal dimension DN2 with relative pressure [greater than] 0.45; the blue dotted line represents relative pressure = 0.45.

Figure 8. Correlation between fractal dimension and SSA (A) and PV (B) of shale samples.

Figure 9. Correlation between fractal dimension and TOC content (A) and thermal maturity of organic matter (B) in Longmaxi shales.

Figure 10. Correlation between fractal dimension and mineral composition of Longmaxi shales.

Figure 11. Relationship between clay mineral composition and fractal dimension of Longmaxi shales.

Table 1

SSA and PV of pores were obtained based on gas adsorption experiments. Four middle and deep shale samples came from the same locations and wells as the samples that were characterized extensively in the previous work (data of BET surface area from Hao et al., 2023) [22].

Sample Number	Low Temperature CO2 Adsorption			Low Temperature N2 Adsorption
	DR Micropore Surface Area	DA Micropore Volume	Mean Equivalent Pore Width	BET Surface Area	BJH Pore Volume	BJH Average Pore Diameter
	(m2/g)	(cm3/g)	(nm)	(m2/g)	(cm3/g)	(nm)
O1	9.4408	0.0051	1.7056	8.8087	0.0117	7.6146
O2	9.8153	0.0052	1.7149	11.3879	0.0092	5.6448
M1	14.7504	0.0068	1.6589	21.2077	0.0185	5.0852
M5	18.2329	0.0094	1.6903	23.2946	0.0211	5.6191
D1	20.7664	0.0087	1.6306	29.3799	0.0260	5.3489
D11	14.1240	0.0069	1.6713	21.7908	0.0222	5.6811

References

1. Zhu, H.J.; Lu, Y.J.; Pan, Y.Y.; Qiao, P.; Raza, A.; Liu, W. Nanoscale mineralogy and organic structure characterization of shales: Insights via AFM-IR spectroscopy. Adv. Geo-Energy Res.; 2024; 13, pp. 231-236. [DOI: https://dx.doi.org/10.46690/ager.2024.09.08]

2. Zou, C.N.; Yang, Z.; Dai, J.X.; Dong, D.Z.; Zhang, B.M.; Wang, Y.M.; Deng, S.H.; Huang, J.L.; Liu, K.Y.; Yang, C. et al. The characteristics and significance of conventional and unconventional Sinian-Silurian gas systems in the Sichuan Basin, central China. Mar. Pet. Geol.; 2015; 64, pp. 386-402. [DOI: https://dx.doi.org/10.1016/j.marpetgeo.2015.03.005]

3. Li, Y.R.; Liu, X.G.; Cai, C.H.; Hu, Z.M.; Wu, B.; Mu, Y.; Duan, X.G.; Zhang, Q.X.; Zeng, S.T.; Guo, J.S. et al. Pore structure characteristics and their controlling factors of deep shale: A case study of the Lower Silurian Longmaxi Formation in the Luzhou area, southern Sichuan Basin. ACS Omega; 2022; 7, pp. 14591-14610. [DOI: https://dx.doi.org/10.1021/acsomega.1c06763] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35557656]

4. Loucks, R.G.; Reed, R.M.; Ruppel, S.C.; Jarvie, D.M. Morphology, genesis, and distribution of nanometer-scale pores in siliceous mudstones of the Mississippian Barnett Shale. J. Sediment. Res.; 2009; 79, pp. 848-861. [DOI: https://dx.doi.org/10.2110/jsr.2009.092]

5. Slatt, R.M.; O’Brien, N.R. Pore types in the Barnett and Woodford gas shales: Contribution to understanding gas storage and migration pathways in fine-grained rocks. AAPG Bull.; 2011; 95, pp. 2017-2030. [DOI: https://dx.doi.org/10.1306/03301110145]

6. Rouquerol, J.; Avnir, D.; Fairbridge, C.W.; Everett, D.H.; Haynes, J.M.; Pernicone, N.; Ramsay, J.D.F.; Sing, K.S.W.; Unger, K.K. Recommendations for the characterization of porous solids (Technical Report). Pure Appl. Chem.; 1994; 66, pp. 1739-1758. [DOI: https://dx.doi.org/10.1351/pac199466081739]

7. Desbois, G.; Urai, J.L.; Kukla, P.A. Morphology of the pore space in claystones–Evidence from BIB/FIB ion beam sectioning and cryo-SEM observations. eEarth; 2009; 4, pp. 1-19. [DOI: https://dx.doi.org/10.5194/ee-4-15-2009]

8. Bu, H.L.; Ju, Y.W.; Tan, J.Q.; Wang, G.C.; Li, X.S. Fractal characteristics of pores in non-marine shales from the Huainan coalfield, eastern China. J. Nat. Gas Sci. Eng.; 2015; 24, pp. 166-177. [DOI: https://dx.doi.org/10.1016/j.jngse.2015.03.021]

9. Liu, S.G.; Ye, Y.H.; Ran, B.; Jiang, L.; Li, Z.; Li, J.; Song, J.; Jiao, K.; Li, Z.; Li, Y. Evolution and implications of shale pore structure characteristics under different preservation conditions. Reser. Eval. Dev.; 2020; 10, pp. 1-11.

10. Jiao, K.; Yao, S.P.; Liu, C.; Gao, Y.Q.; Wu, H.; Li, M.C.; Tang, Z.Y. The characterization and quantitative analysis of nanopores in unconventional gas reservoirs utilizing FESEM–FIB and image processing: An example from the lower Silurian Longmaxi Shale, upper Yangtze region, China. Int. J. Coal Geol.; 2014; 128, pp. 1-11. [DOI: https://dx.doi.org/10.1016/j.coal.2014.03.004]

11. Zhang, J.Z.; Li, X.Q.; Xie, Z.Y.; Li, J.; Zhang, X.Q.; Sun, K.X.; Wang, F.Y. Characterization of microscopic pore types and structures in marine shale: Examples from the Upper Permian Dalong formation, Northern Sichuan Basin, South China. J. Nat. Gas Sci. Eng.; 2018; 59, pp. 326-342. [DOI: https://dx.doi.org/10.1016/j.jngse.2018.09.012]

12. Wang, Y.; Han, D.; Lin, W.; Jia, Y.; Zhang, J.; Wang, C.; Ma, B. Factors Controlling Differences in Morphology and Fractal Characteristics of Organic Pores of Longmaxi Shale in Southern Sichuan Basin, China. Fractal Fract.; 2024; 8, 555. [DOI: https://dx.doi.org/10.3390/fractalfract8100555]

13. Zhang, J.Z.; Li, X.Q.; Zou, X.Y.; Zhao, G.J.; Zhou, B.G.; Li, J.; Xie, Z.Y.; Wang, F.Y. Characterization of the full-sized pore structure of coal-bearing shales and its effect on shale gas content. Energy Fuels; 2019; 33, pp. 1969-1982. [DOI: https://dx.doi.org/10.1021/acs.energyfuels.8b04135]

14. Gou, Q.Y.; Xu, S.; Hao, F.; Yang, F.; Shu, Z.G.; Liu, R. The Effect of Tectonic Deformation and Preservation Condition on the Shale Pore Structure Using Adsorption-Based Textural Quantification and 3D Image Observation. Energy; 2021; 219, 119579. [DOI: https://dx.doi.org/10.1016/j.energy.2020.119579]

15. Li, H.; Zhou, J.L.; Mou, X.Y.; Guo, H.X.; Wang, X.X.; An, H.Y.; Mo, Q.W.; Long, H.Y.; Dang, C.X.; Wu, J.F. et al. Pore structure and fractal characteristics of the marine shale of the Longmaxi Formation in the Changning Area, Southern Sichuan Basin, China. Front. Earth Sci.; 2022; 10, 1018274. [DOI: https://dx.doi.org/10.3389/feart.2022.1018274]

16. Li, X.M.; Wang, Y.R.; Lin, W.; Ma, L.H.; Liu, D.X.; Liu, J.R.; Zhang, Y. Micro-pore structure and fractal characteristics of deep shale from Wufeng Formation to Longmaxi Formation in Jingmen exploration area, Hubei Province, China. J. Nat. Gas Geosci.; 2022; 7, pp. 121-132. [DOI: https://dx.doi.org/10.1016/j.jnggs.2022.06.001]

17. Ma, B.Y.; Hu, Q.H.; Yang, S.Y.; Zhang, T.; Qiao, H.G.; Meng, M.M.; Zhu, X.C.; Sun, X.H. Pore structure typing and fractal characteristics of lacustrine shale from Kongdian Formation in East China. J. Nat. Gas Sci. Eng.; 2021; 85, 103709. [DOI: https://dx.doi.org/10.1016/j.jngse.2020.103709]

18. Jia, A.Q.; Hu, D.F.; He, S.; Guo, X.W.; Hou, Y.G.; Wang, T.; Yang, R. Variations of pore structure in organic-rich shales with different lithofacies from the Jiangdong block, fuling shale gas field, SW China: Insights into gas storage and pore evolution. Energy Fuels; 2020; 34, pp. 12457-12475. [DOI: https://dx.doi.org/10.1021/acs.energyfuels.0c02529]

19. Zeng, Q.C.; Chen, S.; He, P.; Yang, Q.; Guo, X.L.; Chen, P.; Dai, C.M.; Li, X.; Gai, S.H.; Deng, Y. et al. Quantitative prediction of shale gas sweet spots based on seismic data in Lower Silurian Longmaxi Formation, Weiyuan area, Sichuan Basin, SW China. Pet. Explor. Dev.; 2018; 45, pp. 422-430. [DOI: https://dx.doi.org/10.1016/S1876-3804(18)30047-8]

20. Hao, Y.X.; Wu, L.; Jiang, W.; Qian, C.; Zhou, X.; Wang, Y.L. Development characteristics and controlling mechanism of different microfracture combinations in shale reservoir: A case study of silurian longmaxi formation in Weiyuan area. Pet. Res.; 2024; in press [DOI: https://dx.doi.org/10.1016/j.ptlrs.2024.07.003]

21. Zhang, J.R.; Xu, J.T.; Jiang, S.M.; Tang, S. Quantitative identification and distribution of quartz genetic types based on QemScan: A case study of Silurian Longmaxi Formation in Weiyuan area, Sichuan Basin. Pet. Res.; 2021; 6, pp. 423-430. [DOI: https://dx.doi.org/10.1016/j.ptlrs.2021.05.001]

22. Hao, Y.X.; Li, Y.Z.; Zhang, Q.; Jiang, W.; Liang, X.S.; Wang, B.Q.; Lu, Y.J.; Zhu, H.J. Reservoir characterization of the shallow to deep Longmaxi formation in the Weiyuan Block, southwestern Sichuan Basin. Energy Explor. Exploit.; 2023; 41, pp. 2058-2077. [DOI: https://dx.doi.org/10.1177/01445987231188067]

23. Mandelbrot, B.B. Fractal Geometry of Nature, WH Freeman, New York, 1982. Math. Gaz.; 1984; 68, pp. 71-72.

24. Wang, X.Q.; Zhu, Y.M.; Wang, Y. Fractal Characteristics of Micro- and Mesopores in the Longmaxi Shale. Energies; 2020; 13, 1349. [DOI: https://dx.doi.org/10.3390/en13061349]

25. Li, Z.; Liang, Z.K.; Jiang, Z.X.; Gao, F.L.; Zhang, Y.H.; Yu, H.L.; Xiao, L.; Yang, Y.D. The Impacts of Matrix Compositions on Nanopore Structure and Fractal Characteristics of Lacustrine Shales from the Changling Fault Depression, Songliao Basin, China. Minerals; 2019; 9, 127. [DOI: https://dx.doi.org/10.3390/min9020127]

26. Avnir, D.; Jaroniec, M. An isotherm equation for adsorption on fractal surfaces of heterogeneous porous materials. Langmuir; 1989; 5, pp. 1431-1433. [DOI: https://dx.doi.org/10.1021/la00090a032]

27. Jacob, H. Disperse solid bitumens as an indicator for migration and maturity in prospecting for oil and gas. Erdol Kohle Erdgas Petrochem.; 1985; 38, 365.

28. Shan, C.A.; Shi, Y.K.; Liang, X.; Zhang, L.; Wang, G.C.; Jiang, L.W.; Zou, C.; He, F.Y.; Mei, J. Diagenetic characteristics and microscopic pore evolution of deep shale gas reservoirs in Longmaxi Formation, Southeastern Sichuan basin, China. Unconv. Resour.; 2024; 4, 100090. [DOI: https://dx.doi.org/10.1016/j.uncres.2024.100090]

29. Zhang, Z.N.; Lin, M.R.; Xi, K.L.; Li, J.M. Pore development characteristics and controlling factors of Lower Cambrian Qiongzhusi shale gas reservoir in Sichuan Basin, China. Unconv. Resour.; 2024; 4, 100100. [DOI: https://dx.doi.org/10.1016/j.uncres.2024.100100]

30. Shao, X.H.; Pang, X.Q.; Li, Q.W.; Wang, P.W.; Chen, D.; Shen, W.B.; Zhao, Z.F. Pore structure and fractal characteristics of organic-rich shales: A case study of the lower Silurian Longmaxi shales in the Sichuan Basin, SW China. Mar. Pet. Geol.; 2017; 80, pp. 192-202. [DOI: https://dx.doi.org/10.1016/j.marpetgeo.2016.11.025]

31. Everett, D.H.; Koopal, L.K. International union of pure and applied chemistry. Polymer; 2001; 31, 1598.

32. Thommes, M.; Kaneko, K.; Neimark, A.V.; Olivier, J.P.; Rodriguez-Reinoso, F.; Rouquerol, J.; Sing, K.S.W. Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report). Pure Appl. Chem.; 2015; 87, pp. 1051-1069. [DOI: https://dx.doi.org/10.1515/pac-2014-1117]

33. Yang, Y.Y.; Zhang, J.C.; Xu, L.F.; Li, P.; Liu, Y.; Dang, W. Pore structure and fractal characteristics of deep shale: A case study from Permian Shanxi Formation shale, from the Ordos Basin. Acs Omega; 2022; 7, pp. 9229-9243. [DOI: https://dx.doi.org/10.1021/acsomega.1c05779] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/35350342]

34. Nie, W.C.; Zhang, T.S.; Wang, M.W.; Wu, W.; Tan, X.C. Fractal Characteristics and Interfering Factors of Microscopic pores in Marinecontinental Transitional Coal Shale: A case study of the Taiyuan Formation in the northern Qinshui Basin. Acta Sedimentol. Sin.; 2024; 42, pp. 1047-1057. (In Chinese)

35. Zhao, Y.; Li, L.; Si, Y.H.; Wang, H.M. Fractal Characteristics and Controlling Factors of Pores in Shallow Shale Gas Reservoirs: A Case Study of Longmaxi Formation in Zhaotong Area, Yunnan Province. J. Jilin Univ. (Earth Sci. Ed.); 2022; 52, pp. 1813-1829. (In Chinese)

36. Zhang, J.Z.; Xiao, X.; Wang, J.G.; Lin, W.; Han, D.L.; Wang, C.C.; Li, Y.; Xiong, Y.; Zhang, X.C. Pore structure and fractal characteristics of coal-bearing Cretaceous Nenjiang shales from Songliao Basin, Northeast China. J. Nat. Gas Geosci.; 2024; 9, pp. 197-208. [DOI: https://dx.doi.org/10.1016/j.jnggs.2024.03.005]

37. Li, A.; Ding, W.L.; He, J.H.; Dai, P.; Yin, S.; Xie, F. Investigation of pore structure and fractal characteristics of organic-rich shale reservoirs: A case study of lower Cambrian Qiongzhusi formation in Malong block of Eastern Yunnan province, south China. Mar. Pet. Geol.; 2016; 70, pp. 46-57. [DOI: https://dx.doi.org/10.1016/j.marpetgeo.2015.11.004]

38. Wang, D.X.; Zeng, Z.P.; Hu, H.Y.; Wang, T.; Zhu, G.G.; Li, S.T.; Li, L. Fractal characteristics of pore structure of deep continental shale of Lower Wuerhe Formation in central Junggar Basin and its geological significance. Pet. Geol. Recovery Effic.; 2024; 31, pp. 23-35. (In Chinese)

39. Gao, M.; Yang, M.; Lu, Y.; Levin, V.A.; He, P.; Zhu, H. Mechanical characterization of uniaxial compression associated with lamination angles in shale. Adv. Geo-Energy Res.; 2024; 13, pp. 56-68. [DOI: https://dx.doi.org/10.46690/ager.2024.07.07]

40. Zhu, H.; Huang, C.; Ju, Y.; Bu, H.; Li, X.; Yang, M.; Chu, Q.; Feng, H.; Qiao, P.; Qi, Y. et al. Multi-scale multidimensional characterization of clay-hosted pore networks of shale using FIBSEM, TEM, and X-ray micro-tomography: Implications for methane storage and migration. Appl. Clay Sci.; 2021; 213, 106239. [DOI: https://dx.doi.org/10.1016/j.clay.2021.106239]