Fractal Characteristics of Pores in the Longtan Shales of Guizhou, Southwest China

The pore structure of marine-continental transitional shales from the Longtan Formation in Guizhou, China, was investigated using fractal dimensions calculated by the FHH (Frenkel-Halsey-Hill) model based on low-temperature N2 adsorption data. Results show that the overall D1 (fractal dimension under low relative pressure, P/P0 ≤ 0:5) and D2 (fractal dimension under high relative pressure, P/P0 > 0:5) values of Longtan shales were relatively large, with average values of 2.7426 and 2.7838, respectively, indicating a strong adsorption and storage capacity and complex pore structure. The correlation analysis of fractal dimensions with specific surface area, average pore size, and maximum gas absorption volume indicates that D1 can comprehensively characterize the adsorption and storage capacity of shales, while D2 can effectively characterize the pore structure complexity. Further correlation among pore fractal dimension, shale organic geochemical parameters, and mineral composition parameters shows that there is a significant positive correlation between fractal dimensions and organic matter abundance as well as a complex correlation between fractal dimension and organic matter maturity. Fractal dimensions increase with an increase in clay mineral content and pyrite content but decrease with an increase in quartz content. Considering the actual geological evaluation and shale gas exploitation characteristics, a lower limit for D1 and upper limit for D2 should be set as evaluation criteria for favorable reservoirs. Combined with the shale gas-bearing property test results of Longtan shales in Guizhou, the favorable reservoir evaluation criteria are set as D1 ≥ 2:60 and D2 ≤ 2:85. When D1 is less than 2.60, the storage capacity of the shales is insufficient. When D2 is greater than 2.85, the shale pore structure is too complicated, resulting in poor permeability and difficult exploitation.


Introduction
Shale is a type of heterogeneous porous rock with a complex pore structure, including various pore shapes and sizes [1,2]. Currently, the mercury intrusion method, adsorptiondesorption method, and structural fractal method are commonly used to quantitatively analyze shale pore structure characteristics [3][4][5]. Pore fractal theory plays a significant role in studying the complexity of pore structures. The Permian Longtan Formation in Guizhou is a coal-bearing formation containing marine-continental transitional facies, which is generally characterized by high organic matter con-tent and good gas indicators, indicating a great natural gas resource potential [6][7][8][9]. With the development of exploration and research, the evaluation of shale reservoirs has become an important research topic. Reservoir evaluation is one of the key steps to determining the natural productivity and economic value of shale reservoirs. Scientists have found that the Longtan Formation contains a set of shale reservoirs with low porosity (0.89%-2.29%) and permeability (ð0:16 − 29:5Þ × 10 −4 mD), strong heterogeneity, small pore size, and complex pore structure [10]. Using qualitative methods such as polarized light microscopy and scanning electron microscopy, a qualitative understanding of the morphology and structure of the Longtan Formation has been gained [1,10,11]. However, there is limited quantitative research and evaluation of the Longtan Formation pore structure, and a geological parameter to characterize the pore structure well has not yet been identified and incorporated into the reservoir evaluation system. As a result, the pore structure is often neglected in the current reservoir evaluation system.
For conventional sandstone reservoirs, quantitative methods such as the mercury injection capillary pressure (MICP) experiment can be used to study pore structure characteristics [2,12,13]. Tight reservoirs, such as shale reservoirs, have high pore displacement pressure, requiring a higher experiment pressure to measure the pore size. However, high-pressure mercury injection can damage the pore structure of shale [14]. To address this problem, fractal theory, which is an effective approach for studying the irregular surface and heterogeneity of porous materials, was introduced into the study of shale pores [14][15][16][17][18]. Fractal theory considers the complicated pore fracture as a whole and quantitatively evaluates the heterogeneity and irregular surface of pores in shale reservoirs [5,9].
Therefore, this paper systematically studied the pore structures and fractal characteristics of marine-continental transitional facies shales in Guizhou as well as the relationship with other geological parameters (reservoir parameters, organic geochemical parameters, and mineral composition parameters) based on low-temperature N 2 adsorption experiments, field emission scanning electron microscopy (FE-SEM) observations, X-ray diffraction (XRD) analysis of rock mineral composition, organic geochemical experiments, and gas content tests. In this study, the characterization function and geological significance of fractal dimension on pore structure are clarified. Also, the fractal dimension division standard is determined for the dominant shale reservoirs of the Longtan Formation in Guizhou Province, which provides the basis for further exploration, research, and evaluation.

Geological Conditions for Shale Development
The main portion of the study area is located in the Qianzhong Uplift and the depression in the northern Dianqian area, belonging to the Upper Yangtze plate (Figure 1). The regional structure is characterized by NNE-trending and NE-trending folds and faults. The study area is intersected by the Hezhang-Zunyi NE-trending fault to the north and surrounded by the Nayong fault to the southeast [19,20]. Since the formation of the continent in the Middle Permian, the crust has been exposed and eroded. The Longtan Formation, a coal-bearing series of marine-continental sedimentary strata, has been widely deposited in northwest Guizhou. The alternating sedimentary facies combinations, including lagoon facies, tidal-control delta facies, tidal-flat facies, and peat swamp facies, were developed during the Longtan Period [21]. The shale has a small single layer thickness but large cumulative thickness, containing multiple interlayers and coal seams [20,22]. The lithology is dominated by black carbon shale, silty mudstone, sandstone, siltstone, marlite, and coal ( Figure 1).

Samples and Experimental Methods
Samples in this study are all unweathered Longtan core samples from Well-XY1 (X-1 to X-6 in Table 1), Well-FY1 (F-1to  F-3 in Table 1), and Well-JS1 (the locations of the three wells are shown in Figure 1). All samples were taken from gasbearing layers and contain the primary Longtan shale reservoir lithology. The depth and lithology of the samples are listed in Tables 1 and 2. A complete experimental project was conducted, including measurements of organic carbon (TOC) content, kerogen microcomponents, vitrinite reflectance (R o ), XRD analysis of rock mineral composition, argon ion polishing-field emission scanning electron microscopy, low-temperature N 2 adsorption, isothermal adsorption, and gas content analyses (direct method).
The TOC tests were conducted using a LECO-CS230 carbon and sulfur analyzer. The powder samples (100 mg) were treated with 5% HCl (hydrochloric acid) at 80°C to remove inorganic carbon and then washed with pure water to remove residual HCl. The treated samples were placed into the apparatus to measure TOC content. An X'Pert Powder X-ray diffractometer (PANalytical Company, Netherlands) was used to measure the mineralogical compositions of the Longtan Shale samples. Samples were crushed into powders with grain size ranging from 200 to 300 mesh before the XRD analysis. The experiments conformed to the industry standard SY/T5163-2010.
Samples were polished by Argon ion using an Ilion II697 argon-ion polisher (Gatan Company). Then, the polished samples were scanned using a Merlin Compact field emission scanning electron microscope (ZEISS Company) to obtain the micromorphology images with an acceleration voltage of 10.0 kV and working distance ranging from 2 to 15 mm. The experiments conformed to the industry standard GB/T 16594-2008 and SY/T 5162-1997.
Low-temperature N 2 adsorption experiments were performed using a Quadrasorb SI specific surface analyzer. The crushed samples (60-80 mesh) were degassed for 4 h at 150°C. Then, N 2 adsorption experiments were conducted at -196°C under a relative pressure ranging from 0.040 to 0.997. The specific surface area and average pore size were calculated using the Brunauer-Emmett-Teller (BET) method (Brunauer et al., 1938). The experiments conformed to the industry standard GB/T19587-2004.
Isothermal adsorption tests were conducted using a GAI-100 high-pressure gas isothermal adsorption apparatus with a pressure range of 0.007-17.300 MPa at 30°C with SY/T 6132-1995 as the test basis. The desorbed gas content and residual gas content data were directly measured using a tubeless field desorption instrument and a fully sealed residual gas analyzer independently developed by the China

Reservoir Characteristics.
According to the geochemical test results from Longtan shale samples, the TOC of shales ranges from 1.01% to 8.62%, with an average value of 3.68%, indicating that the overall organic matter content is relatively high. R o values primarily range from 2.00% to 3.00% with an average value of 2.61% (Table 1), indicating that Longtan shale is in the early overmature stage with good gas generation conditions. Longtan shales are primarily composed of quartz, feldspar, carbonate minerals, and clay minerals. The quartz content ranges from 10.46% to 38.19% with an average value of 28.99%, and clay mineral content ranges from 25.94% to 47.37% with an average value of 40.37%, which is relatively large. In addition, clay minerals are primarily composed of illite/montmorillonite and illite, while chlorite, kaolinite, and montmorillonite account for a small proportion (Table 1).
Through FE-SEM observations, Longtan shale pores can be divided into four types: inorganic intergranular pores, inorganic intragranular pores, organic pores, and microfractures based on their relationships with grain and pore morphology. Inorganic intergranular pores are mostly intercrystalline pores and shrink fractures along the grain (Figures 2(a) and 2(f)), with large pore sizes ranging from mesopores (2-50 nm) to macropores (≥50 nm). With simple structure and good connectivity, inorganic pores are primarily intercrystalline pores between clay minerals and dissolution pores (Figures 2(b) and 2(c)). The intercrystalline pores of clay minerals are mostly slit-shaped with good connectivity, and dissolution pores are mostly round or irregular with relatively poor connectivity, including both micropores (<2 nm) and macropores. Both the organic abundance and maturity can control the development of organic pores. In the Guizhou area, Longtan shales have high organic abundance, and the maturity is primarily in the early overmature stage. Organic pores are mostly round and elliptical in shape     6 Geofluids with relatively poor connectivity (Figures 2(g), 2(h), and 2(i)), including both micropores and macropores. Microfractures are most likely related to tectonic activity and commonly appear within brittle mineral crystals (Figures 2(a), 2(g), and 2(h)). They play an important role in increasing pore connectivity and improving the reservoir properties of the Longtan Formation. Low-temperature N 2 adsorption-desorption experiments show that the specific surface area of Longtan shales ranges from 8.32-31.18 m 2 /g (average 15.79 m 2 /g). The proportion of micropores is high, primarily distributed from 3 nm to 5 nm (Figure 3), but there are also some mesopores and macropores larger than 25 nm. Adsorption-desorption curves show that the adsorption volume of the Longtan shales in the low-pressure region is small, and the slopes of the curves vary without any significant inflection points. The higher the relative pressure is, the larger the adsorption volume is. Capillary condensation of the adsorbate occurs, and the isotherm rises rapidly. Desorption lag occurs due to the capillary force. According to the IUPAC classification [23][24][25][26][27][28], the increasing hysteresis is H2 type and H3 type (Figure 4), indicating that quite a few flaky grains, primarily clay minerals, are present within the shale. Pores are primarily slit, wedge, and ink bottle-shaped [4,11,26].

Shale
Pore Fractal Dimension. Pore fractal dimensions were calculated based on the fractal FHH (Frenkel-Halsey-Hill) model using low-temperature N 2 adsorption data for the Longtan shale (Table 2) [26,[28][29][30]. The calculation formula is where V-the volume of adsorbed gas at the equilibrium pressure P, cm 3 /g; P 0 -saturated vapor pressure, MPa; P -equilibrium pressure, MPa; D-fractal dimension.    8 Geofluids According to the fractal FHH model, D (fractal dimension) can be determined by the slope of the fitting line in the plot of LnV − Ln½LnðP 0 /PÞ. Generally, D ranges from 2 to 3 [31,32]. When D is closer to 2, the pore structure is simple with a smooth and regular surface. On the other hand, when D is closer to 3, the pore structure is complex with an irregular surface, strong heterogeneity, and strong fluid flow resistance. A high fractal dimension usually means a complex pore structure, which is more favorable for gas adsorption and storage than for gas transport [25,26].
The piecewise least-square fitting line obtained from the experimental data reflects two different fractal characteristics in the shale pores (Table 2) ( Figure 5). The fractal dimension value calculated using a curve with relatively low pressure (P/P 0 ≤ 0:5) was recorded as D1, and the fractal dimension calculated using a curve with relatively high pressure was recorded as D2 (P/P 0 > 0:5). The plots of ln ðVÞ versus ln ½ ln ðP 0 /PÞ are shown in Figures 5 and 6. D1 ranges from 2.6655 to 2.8648 with an average value of 2.7426, and D2 ranges from 2.6841 to 2.9256 with an average value of 2.7838. D1 and D2 are large and close to 3. Also, D2 is greater than D1 (Figure 6).

Characterization Function of Fractal Dimensions.
The correlation between the calculated fractal dimensions and the specific surface area (Figure 7(a)) as well as the average pore size (Figure 7(b)) is examined to determine the fractal dimension characterization function of the pore structures and shale storage properties. D1 and D2 increase with the increase in specific surface area and decrease in pore size. The correlation between D1 and specific surface area is slightly better than that of D2, while the correlation between D2 and average pore size is slightly better than that of D1. D1 is more effective for comprehensively characterizing the shale adsorbed gas storage capacity, while D2 can effectively characterize pore structure complexity and reservoir heterogeneity. Shale isothermal adsorption tests showed that the maximum adsorption gas volume has a significant positive correlation with D1 (Figure 7(c)), which further verifies the ability of D1 to characterize the gas adsorption and storage capacity of shales. According to the D1 and D2 values for the marine-continental transitional facies Longtan shales in the Guizhou area, the overall adsorbed gas adsorption and storage capacity is good, indicating that the Longtan shales are a good reservoir for adsorbed natural gas. However, the pore size is small, and the pore structure is complex with relatively poor connectivity.

Relationship between Fractal Dimensions and Organic
Geochemical Characteristics. Shale is typically rich in organic matter. The nanomicroorganic pores present in the organic matter are important storage spaces for gas [22,33,34]. Therefore, a significant relationship exists between the organic geochemical characteristics and fractal dimensions. By analyzing the correlation between fractal dimensions and TOC (Figure 8(a)) as well as R o (Figure 8(b)), it is found that a good positive correlation exists between fractal dimen-sions and TOC. The fractal dimensions increase with increasing organic matter abundance because the organic pores and clay mineral-related inorganic pores are the most important type of shale reservoirs. In marine-continental transitional facies shales, organic matter is commonly associated with clay minerals, indicating that both organic pores and inorganic pores are well developed in organic-rich shales. All these pores have small diameters and complex structures resulting in a significant increase in fractal dimensions. The correlation between fractal dimensions and R o is not obvious. The fitting lines show that when R o ranges from 2.0-2.5%, fractal dimensions increase with increasing R o . D1 and D2 both reach the peak when R o is around 2.5%, then fractal dimensions show a negative correlation with R o . However, the two fitting line confidences are low, because the type-III kerogen is still in thermal pyrolysis in the early overmature stage, and organic pores can be developed along with gas generation. The development of the organic pores determines the increase in fractal dimensions. However, along with this process, the graphitization of organic matter also occurs [35], which reduces the adsorption capacity of shales and even collapses the graphitized organic pores. Under the simultaneous influence of these two effects, the fractal dimension and the organic maturity show a complicated relationship. The specific change trend of the fractal dimensions is related to the relative strength of these two effects. When the thermal pyrolysis gas generation dominates, fractal dimensions increase. Conversely, when graphitization dominates, fractal dimensions decrease.

Relationship between Fractal Dimensions and Mineral
Components. As different minerals develop pores with different structures, the mineral composition of shales is also an important factor influencing fractal dimensions. Quartz and clay minerals are the primary minerals within the Longtan shales. Fractal dimensions are negatively correlated with quartz content (Figure 9(a)) because the Longtan Formation is a set of marine-continental transitional shales, and the quartz contained therein is primarily terrestrial quartz. Therefore, organic abundance is negatively correlated with quartz content (Figure 10). Furthermore, the grain size of quartz minerals is relatively large. Hence, pores related to quartz are intergranular pores and microfractures (macropores to mesopores) with simple structures. The increase in the quartz content results in an increase in simple macropores in shales, causing a decrease in fractal dimensions. On the contrary, fractal dimensions have a good positive correlation with clay mineral content (Figure 9(b)). As previously mentioned (Section 4.2), the organic abundance in marine-continental transitional shales is positively correlated with clay mineral content (Figure 10), indicating that shales rich in clay minerals are also organic-rich. Thus, inorganic as well as organic micropores with complex structures can be developed in these shales. Shales rich in clay minerals have strong gas adsorption and storage capacity, with complex pore structures and strong heterogeneity with large fractal dimensions. In addition to quartz and clay content, pyrite content also has a significant effect on the fractal dimension (Figure 9(c)). Numerous studies have shown that pyrite   10 Geofluids primarily develops in an oxygen-deficient environment, which is conducive to the preservation of organic matter [6,[36][37][38]. Organic abundance shows a good positive correlation with pyrite content (Figure 10). Framboid pyrites, a type of pyrite which predominantly influences pore structures [39,40], are the primary type found in Longtan shales. Intercrys-talline pores are developed inside framboid pyrites and are commonly filled with organic matter (Figures 2(d) and 2(e)). Pyrite crystals can serve as supporting frameworks to protect organic matter and organic pores within them [22,36,41,42]. Therefore, the shale samples with large pyrite content in this study contain abundant organic matter and   Figure 9: Correlation between fractal dimensions and mineral content of Longtan shales. 12 Geofluids well-developed organic pores, thus having a large fractal dimension.

Geological Significance of Fractal Dimensions
As mentioned above, the fractal dimension can be used as an effective quantitative characterization parameter for pore structure, gas adsorption, storage capacity, and pore complexity of shales in shale reservoir evaluations. D1 can reflect the gas adsorption and storage capacity of shales. Shales with larger D1 have a stronger gas adsorption capacity and are better natural gas reservoirs, especially for adsorbed gas. D2 can characterize pore structure complexity and heterogeneity. Shales with larger D2 have a higher proportion of micropores, more complex pore structures, and strong heterogene-ity. All these will reduce the permeability of shales and make gas desorption and diffusion more difficult, thus impeding gas flow in the shale reservoir [14,[43][44][45][46][47]. Therefore, for evaluating shale gas potential, the larger the D1 value is, the better the reservoir properties of the shale, while D2 should be in the appropriate range to ensure that the reservoir is not too complex for exploitation. In the reservoir evaluation process, D1 should have a lower limit, and D2 should have an upper limit [22], such that a favorable reservoir characterized by fractal dimension would also have good gas adsorption, good storage capacity, and an acceptable pore structure complexity [48][49][50][51]. The gas content ratio of natural desorption (the sum of lost gas content and desorbed gas content) to the total gas content (the sum of lost gas content, desorbed gas content, and residual gas content) can   13 Geofluids be regarded as the approximate proportion of gas that can be produced naturally during the exploitation process (with no reservoir fracture reconstruction). Since the lost gas content is obtained mathematically, there is a certain error compared to the actual value. However, the ratio has a certain significance for the current analysis. A larger ratio means more gas produced naturally and lower exploitation difficulty [49,52,53]. Correlation between the ratio and D2 (Figure 11) indicates that when D2 exceeds 2.85, the proportion of desorbed gas tends to decrease.
Combined with isothermal adsorption test data, favorable reservoir evaluation criteria of Longtan shales in Guizhou can be formulated. The lower limit of D1 is set as 2.60. When D1 is less than 2.60, the gas adsorption and storage capacity of shale are insufficient. The upper limit of D2 is set as 2.85. When D2 is larger than 2.85, the proportion of desorbed gas in the shale decreases, and the pores become too complex. Consequently, gas productivity can be affected. When the clay mineral content of the shale is greater than 40.0% (Figure 9(a)) and the quartz content is less than 30.0% (Figure 9(b)), the shale brittleness is poor, which can hinder hydraulic fracturing [44]. Exploitation of this kind of shale (D2 > 2:85) requires a more detailed recoverability evaluation and complex fracture scheme. (2) Both D1 and D2 show positive correlations with specific surface areas and negative correlations with pore size. D1 also shows a good positive correlation with the maximum gas absorption capacity of the shale. D1 and D2 increase with increasing organic matter and have complex correlations with organic maturity. There are positive correlations between fractal dimensions and clay mineral content and pyrite content, as well as a negative correlation between fractal dimensions and quartz content

Conclusions
(3) For the set of marine-continental transitional shales of the Longtan Formation in Guizhou, the lower limit of D1 is set as 2.60, and the upper limit of D2 is set as 2.85. When D1 is less than 2.60, the gas adsorption and storage capacity of the shale are insufficient.
When D2 is larger than 2.85, the shale pores are so complex that the permeability is poor and natural productivity is low, indicating that the recoverability of the shale reservoir requires further evaluation

Data Availability
The data used to support the findings of this study are included within the article and are available from the corresponding author upon request.