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. 2021 Nov 10;6(46):30889–30900. doi: 10.1021/acsomega.1c02539

Fractal Characteristics and Significance of Different Pore Types of the Wufeng–Longmaxi Formation, Southern Sichuan Basin, China, Based on N2 Adsorption and Image Analysis

Yang Chen †,*, Hongming Tang †, Majia Zheng †,‡, Changsheng Li †, Shengxian Zhao ‡, Ning Zhao †, Yijiang Leng †
PMCID: PMC8613811  PMID: 34841132

Abstract

graphic file with name ao1c02539_0014.jpg

Shale gas is an important unconventional natural gas resource, and its reservoirs have pores with strong heterogeneity, which have an important effect on the adsorption and migration of shale gas, but the specific mechanism is still unclear. To further clarify the pore structure characteristics of shale gas reservoirs and the mechanism of their influence on CH4 adsorption capacity, marine shale samples from the Wufeng–Longmaxi formation of wells N1, N3, and N10 in Changning block, southern Sichuan Basin, China, were selected for total organic carbon (TOC), X-ray diffraction (XRD), N2 gas adsorption (N2-GA), CH4 gas adsorption (CH4-GA), and field emission scanning electron microscopy (FE-SEM). The Frenkel–Halsey–Hill (FHH) model and Slit Island Analysis (SIA) were used to calculate the fractal dimension of the pore system and different types of pores, and their relationship and influence on CH4 adsorption capacity were also discussed. The results show that the fractal dimension could reflect the complexity and heterogeneity of pores. According to the FHH model, fractal dimensions of the surface and structure of the pore system (D1 and D2, D1 < D2) were obtained, and the pore structure was more complex than the pore surface. According to SIA, the surface fractal dimensions of four types of reservoir space (DDP, DOP, DIP, and DMF) decrease progressively, and their main body is 2.60–2.80, 2.40–2.65, 2.20–2.40, and 2.05–2.30. Organic pores and intergranular pores are the most abundant, and so D1 is mainly related to DOP and DIP. In high-TOC samples, D1 is close to DOP, while in low-TOC samples, D1 is close to DIP. The complexity of the pore surface, D1, and specific surface area have a positive correlation, and with the increase of pore surface complexity, methane adsorption capacity could be significantly improved. Therefore, D1 may be used as a characterization parameter of CH4 adsorption capacity, which could provide some evidence to further clarify the adsorption mechanism of shale gas.

1. Introduction

With the advance of theory and technology, shale has changed from a nonreservoir to an unconventional oil and gas reservoir, which has typical characteristics such as self-storage and abundant nanoscale pores.1−5 According to the International Union of Pure and Applied Chemistry (IUPAC), the pores in shale are divided into micropores (<2 nm), mesopores (2–50 nm), and macropores (>50 nm).6 In addition, according to their morphology and development position, they are also divided into organic pores (OPs), intergranular pores (IPs), dissolution pores (DPs), and microfractures (MFs).4,7−9

Pore structure characteristics (pore size, volume, area, shape, connectivity, and spatial distribution) are key parameters to evaluate the quality of shale gas reservoirs because they play an important role in controlling the gas content and permeability.2,7,10 Previous studies have been carried out by a variety of methods, such as field emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), nm and μm CT, etc., which are mainly based on microscopic imaging techniques.8,11−14 In addition, high-pressure mercury injection (HPMI),15−17 nuclear magnetic resonance (NMR),18−21 CO2 and N2 gas adsorption (N2-GA),6,10,22−24 and other quantitative techniques were also used widely. In addition, the semiquantitative technology based on a combination of high-resolution imaging technology and image software is another useful method.4,13,14,25 However, the results of FE-SEM, TEM, and CT methods are significantly affected by the size of the observation field.8,26 Although HPMI, NMR, and CO2 and N2 gas adsorption could quantitatively describe pore size distribution, they are not suitable for microscopic observations.15 The semiquantitative method is also affected by the image resolution and the number of statistical samples.8 Therefore, it is necessary to combine various methods to characterize the pore structure characteristics of shale.26,27

Fractal theory is another effective method to study the characteristics of the pore structure, which was formally proposed by Mandelbrot in 1975 and widely used to study the self-similarity of various substances in nature.28−30 Fractal dimensions have been proved to be a useful and reliable petrophysical parameter for describing and quantifying irregular solid pore structures and complex surfaces.31 Pores of oil and gas reservoirs such as sandstone, coal rock, and shale have fractal characteristics, and many scholars applied fractal theory and fractal dimensions to study reservoir pores.27,32−35 Many methods/models have been proposed and used by predecessors, such as the box-counting method, which is based on the two-dimensional casting of thin sections, SEM and three-dimensional nm−μm CT images,8,36 the Frenkel–Halsey–Hill (FHH) model based on low-pressure N2 adsorption,37,38 the Brooks–Corey model based on mercury injection data,37,39,40 and models based on NMR data.41−45 Among them, the FHH model has been widely used and confirmed in previous research studies due to its simplicity, convenient calculation, and relatively reliable results,46 and a lot of achievements have been made.8,26,45,47−51 However, it is not suitable for calculating the fractal dimension of different types of pores. There are significant heterogeneity and differences among different types of pores in shale,1,12,15 leading to differences in the reservoir properties of shale,15,27 which have an important influence on shale gas storage capacity (free gas and adsorbed gas).52,53 Therefore, it is necessary to find a method to study various complex pores in shale and figure out their influence on shale gas adsorption capacity and control mechanism.

Mandelbrot proposed a method for calculating the fractal dimension of a steel section (fractal surface), which is called Slit Island Analysis (SIA) and might be used to study shale pores. The fractal dimension of the steel section could be calculated through a two-dimensional image by this method.30 Combined with this method and high-definition image analysis technology, the fractal dimension of different types of reservoir space and the fractal dimension calculated by the FHH equation are analyzed, and their relationship is discussed in this paper. Finally, the relationship between the fractal dimension and CH4 adsorption capacity of shale is also studied. The research results should be of great significance for further understanding the pore heterogeneity of shale gas reservoirs and their influence on CH4 adsorption capacity.

2. Geological Setting

Sichuan Basin is in the west of the Yangtze Platform, surrounded by different types of mountain structures, such as Dalou Mountain in the east. With an area of 1.8 × 105 km2, it is one of the most important oil and gas exploration and development zones in China (Figure 1a,b).2,43,51,54,55 Marine shale of the upper Ordovician Wufeng formation (O3w) and the lower Silurian Longmaxi formation (S1l) is widely distributed in southern, eastern, northeastern, and western Sichuan, among which, it is well developed in southern Sichuan with an average thickness of more than 100 m.2,43 The Wufeng formation and the bottom of the Longmaxi formation comprises black shales rich in organic matter and graptolite, and their kerogen is mainly of the sapropel type.2,43,56

Figure 1.

Figure 1

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Location, tectonic setting, sedimentary background, and stratigraphy of the study area. (a) Geographical location of the Sichuan Basin. (b) Tectonic location and sedimentary background of the study area. (c) Simplified formation histogram of well N10.

Total organic carbon (TOC) in the top of the Wufeng formation and the bottom of the Longmaxi formation is relatively high. As the buried depth becomes shallower, TOC, siliceous, and calcareous mineral content decrease gradually, while the content of clay minerals increases (Figure 1c).

3. Samples and Methods

3.1. Sample Collection

The samples used in this study are all from drilled wells (N1, N3, and N10) in Changning block, southern Sichuan Basin, China, belonging to the Wufeng and Longmaxi formation. The sedimentary background is a deep-sea shelf facies (Figure 1b), and the main feature is black shale, containing a lot of graptolite fossils and rich in bedding. Experiments (TOC, X-ray diffraction (XRD), FE-SEM, etc.) were all carried out in the State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University.

3.2. Experimental Methods

3.2.1. TOC and XRD

According to the Chinese national standard (GB/T 19145-2003) and using a CS230HC carbon and sulfur analyzer, TOC was analyzed. Before the experiment, shale samples were milled to 120–200 mesh, and chloroform was extracted. After this, they were mixed with 5% dilute hydrochloric acid to remove carbonate components, and then they were washed with distilled water. Finally, these samples were dried at 70 °C for 12 h and placed in the instrument to measure the TOC.

The XRD experiment was conducted using a Bruker D8 ADVANCE diffractometer according to Chinese industry standard (SY/T5163-2010). Before the experiment, the samples were ground into powder, and the mass of samples was greater than 30 mg.

3.2.2. N2 Gas Adsorption Analysis

The low-pressure N2 gas adsorption experiment was conducted in accordance with the Chinese national standard (GB/T 5751-2009), and the Nova 2000e automatic N2 adsorption instrument (Quantachrome Company, Boynton Beach, FL) was used. The samples were prepared into particles of about 3 mm and then dried at 110 °C for 24 h for degassing. After naturally cooling down, N2 gas was used as an adsorption gas to obtain the adsorption and desorption isotherm. The Brunauer–Emmett–Teller (BET) model was used to calculate the specific surface area,8,57 and the Barret–Joyner–Halenda (BJH) model was applied to calculate the pore volume and pore size distribution based on N2 adsorption data,58−60 which could effectively characterize the pore distribution characteristics of mesopores in shale.15,17,61

3.2.3. CH4 Gas Adsorption Analysis

CH4 gas adsorption experiment was carried out in accordance with the Chinese energy industry standard (NB/T10117-2018), and the magnetic levitation balance gravimetric high-pressure adsorption isotherm was obtained using IsoSORP-HP (Rubotherm Company, Germany). The maximum test temperature of the instrument is 150 °C, and the maximum test pressure is 70 MPa. Before the experiment, the samples were crushed to the range of 182–450 μm and dried at 110 °C for 24 h. Then, CH4 gas at a concentration of 99.99% was used for adsorption and analytical experiments at 75.5 °C.

3.2.4. FE-SEM

The surface to be observed was initially polished with sandpaper and then polished under a Leica EM TIC 3X argon ion polishing machine (Leica Microsystems Limited, Germany). After polishing, the surface was gold-plated and then observed under an FEI Quanta 650 FEG scanning electron microscope, and all kinds of pores in the field of view were photographed and preserved. At the same time, energy-dispersive X-ray spectroscopy (EDS) was also used to identify minerals and organic matter and obtain information on shale pore types and organic petrography.

3.3. Fractal Calculation Theory and Method

3.3.1. Frenkel–Halsey–Hill Model

The Frenkel–Halsey–Hill model based on N2 adsorption has been widely used to calculate the fractal dimension of coal and shale pores since it was proposed.10,22,26,33,43−45,49,62,63 Its specific equation is as follows

3.3.1. 1
3.3.1. 2

where P is the equilibrium pressure in the N2 gas adsorption process (MPa), P0 is the saturated vapor pressure of the gas (MPa), V is the adsorption volume of N2 at each equilibrium pressure (cm3/g), k is the slope of the fitting line between ln(P/P0) and ln V, C is a constant, and D is the fractal dimension based on N2 adsorption.

According to the difference of N2 molecular adsorption behavior in different pressure ranges, the fitting curves of ln V and ln(ln(P/P0)) are usually divided into two fitting intervals (P/P0 < 0.45 and P/P0 > 0.45); thus, the fractal dimensions D1 and D2 would be obtained.10,22,26,33,43,44,51,62−64D1 and D2 reflect the roughness of the pore system surface and the complexity of the pore structure, respectively.26,33,51,63,64

3.3.2. Slit Island Analysis

Using the software 3DMAX, according to the definition and introduction of Slit Island Analysis (SIA) in Mandelbrot's paper, the principle diagram of calculating the fractal dimension of the fractal surface was drawn (Figure 2). A series of “islands” surrounded by nickel are obtained by plating nickel on the steel section and polishing it parallel to the steel section, which are called “Slit Islands” (Figure 2a–d). The fractal dimension of this section is D at the beginning, and the fractal dimension of the “Slit Island” contour obtained after polishing is D′. Based on the double logarithmic coordinates of the perimeter and area of slit islands, an inclined line with slope D′ will be obtained, and D is equal to D′ + 1.30

Figure 2.

Figure 2

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Schematic diagram of fractal dimension calculations of the fractal surface by SIA. (a) Tensile fracture morphology of steel. (b) Model of the tensile fracture morphology. (c) Horizontal cutting of the metal section model. (d) Model of slit islands. (e) Three-dimensional model of porous rock.

Both the steel section (Figure 2a) and rock surface (Figure 2e) are fractal surfaces,27,30 and they have some similar characteristics. Pores and skeleton particles could be compared to bumps and dimples in steel sections, respectively. Therefore, SIA may be used to calculate the fractal dimension of the porous rock surface. The rock is composed of skeleton particles and pores, and the fractal dimension of the rock surface is also the fractal dimension of skeleton particles, while the fractal dimension of skeleton particles is equal to that of pores.

Image-pro Plus is an image processing software for quantitative analysis, which is widely used in biological and medical fields. Using this software, a series of geometrical characteristics of a selected area could be calculated, such as circumference, area, angle, and the ratio of the major axis to the minor axis. In this work, the flow chart of pore extraction and fractal dimension calculation is shown in Figure 3. These high-definition pore image photos were taken using an FE-SEM, and then they were imported into this software for extracting pores. After manually selecting pores one by one, scale calibration and measurement options selection (area, perimeter, and the ratio of the major axis to the minor axis) were performed. After this, information of pores was exported to Excel software, and formulas 3 and 4 were used for calculation and correlation analysis. Finally, the fractal dimensions of different types of shale pores were obtained.

3.3.2. 3
3.3.2. 4

where S is the area of a single pore (μm2), L is the perimeter of a single pore (μm); D′ is the slope of the inclined straight line, C′ is a constant, and D is the fractal dimension calculated by the SIA.

Figure 3.

Figure 3

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Process of extracting different types of pores and calculating fractal dimensions.

4. Results

4.1. Material Composition Characteristics

The distribution and characteristics of organic matter and various minerals could be clearly observed by FE-SEM. Organic matter is often black or dark gray with different shapes, and pores within it are called organic pores (Figure 4a). Its element composition is characterized by a large amount of the C element (Figure 4d). Quartz minerals are divided into authigenic quartz and terrigenous quartz according to their source and genesis, and they have significantly different characteristics.65,66 Clay minerals are widely distributed, with small particles and different shapes, and intergranular pores are often developed in them (Figure 4b). The EDS results show that shale mainly consists of Al, Si, O, Mg, and K elements (Figure 4e). Calcite, feldspar, and dolomite minerals are relatively rare, with large particles, partially dissolved, and often surrounded by clay minerals (Figure 4c). The feldspar is mainly composed of Al, Si, O, and K elements (Figure 4f).

Figure 4.

Figure 4

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Characterization of shale composition based on FE-SEM and EDS. (a) Sample 10, organic matter and organic pores; (b) sample 3, clay and intergranular pores; (c) sample 1, feldspar and dissolution pores; and (d–f) element distribution of (a–c).

The results of TOC and XRD experiments show that the TOC of wells N1, N3, and N10 are 0.97–6.03, 2.25–4.77, and 1.19–4.30%, respectively, with an overall average of 2.85%. Quartz and clay minerals have the highest relative content, with an average of 40.58 and 31.34%, respectively, followed by calcite, feldspar, and dolomite, with an average of 12.48, 9.66, and 5.94%, respectively (Table 1).

Table 1. Depth, TOC, Relative Mineral Composition, Specific Surface Area, Specific Pore Volume, and Fractal Dimensions of Shale Samples.

                    fractal dimension
well depth (m) strata sample ID TOC (%) siliceous minerala (%) calcareous mineralb (%) total clayc (%) specific surface area (m2/g) specific pore volume (cm3/g) D1 D2
N1 2480.50 S1l 1 0.97 49.46 11.10 39.45 9.97 0.0087 2.52 2.86
N1 2481.70 S1l 2 1.39 66.60 23.07 10.33 10.02 0.0100 2.43 2.85
N1 2487.16 S1l 3 1.11 54.61 13.19 32.21 10.34 0.0103 2.59 2.85
N1 2491.92 S1l 4 1.15 37.70 19.64 42.66 14.10 0.0133 2.61 2.87
N1 2495.90 S1l 5 2.01 45.57 8.65 45.77 19.23 0.0168 2.61 2.86
N1 2508.90 S1l 6 4.17 49.76 19.61 30.63 24.76 0.0219 2.66 2.86
N1 2512.20 S1l 7 2.69 55.08 24.43 20.49 13.78 0.0124 2.57 2.84
N1 2523.35 O3w 8 6.03 27.80 37.62 34.59 21.93 0.0219 2.63 2.83
N3 2367.90 S1l 9 2.25 43.44 4.94 51.61 24.28 0.0180 2.39 2.87
N3 2379.50 S1l 10 4.77 52.68 29.48 17.83 27.96 0.0220 2.56 2.86
N3 2386.76 S1l 11 3.73 63.16 22.55 14.3 36.71 0.0370 2.53 2.85
N10 2161.90 S1l 12 1.19 44.08 13.68 42.22 12.75 0.0117 2.34 2.85
N10 2176.26 S1l 13 1.29 43.26 14.81 41.93 13.35 0.0127 2.32 2.86
N10 2189.85 S1l 14 1.59 45.13 12.18 42.7 12.65 0.0107 2.42 2.87
N10 2194.66 S1l 15 2.41 42.39 7.15 50.46 17.64 0.0150 2.50 2.86
N10 2211.06 S1l 16 2.30 43.33 7.33 49.34 16.50 0.0136 2.48 2.88
N10 2214.63 S1l 17 2.14 29.74 21.15 49.11 15.47 0.0125 2.52 2.85
N10 2218.94 S1l 18 3.41 49.13 16.72 34.15 24.56 0.0205 2.57 2.87
N10 2220.26 S1l 19 4.59 58.53 16.18 25.29 25.08 0.0209 2.57 2.86
N10 2222.26 S1l 20 4.13 56.98 18.76 24.25 24.01 0.0193 2.53 2.87
N10 2223.84 S1l 21 4.04 57.78 26.06 16.16 18.61 0.0152 2.58 2.85
N10 2224.61 S1l 22 3.80 54.55 27.22 18.23 23.61 0.0195 2.57 2.87
N10 2226.26 S1l 23 3.81 63.70 17.30 19.01 19.53 0.0179 2.50 2.84
N10 2233.86 S1l 24 4.30 72.71 18.44 8.85 23.13 0.0204 2.56 2.83
N10 2238.16 O3w 25 4.08 57.44 31.00 11.56 16.88 0.0152 2.52 2.82
average 2.85 50.58 18.49 5.94 19.07 0.0167 2.52 2.86
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a

Siliceous mineral includes quartz and feldspar.

b

Calcareous mineral includes dolomite and calcite.

c

Total clay includes all types of clay minerals, such as illite and chlorite.

4.2. Pore Structure Characteristics

Various types of reservoir spaces were observed by FE-SEM, of which organic pores, intergranular pores, dissolution pores, and microfractures were the most common, and the morphology, size, and content of different types of pores are quite different (Figures 3 and 4).4,7−9 In previous studies, the pore size extracted by image software was usually converted into a diameter of a circle of equal area to study size distribution characteristics.4,25,67 However, pores are more like ellipses with different long and short axis lengths when compared to circles. Therefore, the lengths of the major axis and minor axis of ellipses with the same area as pores and the same long/minor axis ratio are used to accurately characterize the true pore size in this paper. The specific formula is as follows

4.2. 5
4.2. 6

where A is the length of the major axis of the equivalent ellipse (nm), B is the length of the minor axis of the equivalent ellipse (nm), c is the major axis/minor axis ratio, which could be obtained by Image-pro Plus, and S is the equivalent ellipse area, which also could be extracted by Image-pro Plus (nm2).

Using this method, the length and width of typical pores were obtained and analyzed (Figure 5). Due to the resolution and magnification of FE-SEM, all of these pores are larger than 10 nm. The pore width distribution of organic pores and intergranular pores is consistent, decreasing from 20–30 nm to a larger region, while dissolution pores and microfractures have opposite trends (Figure 5a). The length distribution of these four types of pores is completely different. Organic pores and intergranular pores have no significant main peak, ranging from 30–40 to 150–200 nm, while dissolution pores are distributed in four intervals, with a peak (>200 nm) accounting for about 60%, and the long axis length of microfractures are all above 200 nm (Figure 5b). It should be noted that these pore size distributions cannot fully characterize real pore size characteristics.8 However, the fractal dimension is an inherent feature of the pores and has nothing to do with the pore size involved in statistics.27

Figure 5.

Figure 5

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Distribution of the width and length of different types of pores in Figure 2. (a) Equivalent ellipse minor axis length distribution; (b) equivalent ellipse major axis length distribution.

According to N2-GA results, types of hysteresis loops are type H2 and H4 (Figure 6a), and type H4 corresponds to narrow slitlike pores, while type H2 corresponds to complex pore types.6 With the increase of TOC, hysteresis loops change from type H4 to type H2, showing that samples with different TOC have distinct differences in the pore structure. To minimize the impact of Tensile Strength Effect (TSE), the BJH model and adsorption branch of these isotherms were used for pore size calculations.50,59 Pore diameter is mainly in the range of 3–20 nm, belonging to the mesoporous pores (Figure 6b). Specific surface and specific pore volume range from 9.97 to 36.71 m2/g and 0.0087 to 0.370 cm3/g, with an average of 19.07 m2/g and 0.0167 cm3/g, respectively (Table 1).

Figure 6.

Figure 6

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Low-pressure N2 gas adsorption results of eight samples with different TOC from N1. (a) N2 gas adsorption and desorption isotherms; (b) pore size distribution based on the BJH model and applied to the branch of adsorption isotherms.

4.3. Fractal Dimension

4.3.1. Fractal Dimensions from N2 Gas Adsorption

N2 molecules have different adsorption behaviors in different pressure ranges. When P/P0 < 0.45, it is a monolayer adsorption process dominated by van der Waals (VDW) force, and when P/P0 > 0.45, it is a capillary condensation process controlled by surface tension (Figure 6a).26,33,44 Therefore, the relationship curve between ln V and ln(ln(P0/P)) is also divided into two fitting curves, and fractal dimensions (D1 and D2) are also calculated, respectively. R2 of these fitting lines is all above 0.90, which indicates that pores have fractal characteristics (Figure 7). Fractal dimensions of N1, N3, and N10 calculated by FHH are shown in Table 1. D1 is between 2.32 and 2.66, with an average value of 2.53, and D2 is significantly larger than D1, ranging from 2.82 to 2.88, with an average value of 2.85. D2 is significantly larger than D1, indicating that the complexity of the pore structure is higher than that of the pore surface.26,33,45,51

Figure 7.

Figure 7

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Plots of ln(V) vs ln(ln(P0/P)) reconstructed from N2-GA isotherms of eight samples from well N1. (a) Sample 1; (b) sample 2; (c) sample 3; (d) sample 4; (e) sample 5; (f) sample 6; (g) sample 7; (h) sample 8.

4.3.2. Fractal Dimensions from SIA

Plots of log(perimeter) and log(area) of typical solution pores, organic pores, intergranular pores, and microfractures in Figure 2 show a strong positive correlation, with an R2 of 0.9917, 0.9516, 0.9596, and 0.8819, respectively, which is consistent with the findings of Mandelbrot.30 It is proved that the surface of the four types of pores have fractal characteristics, and this method can be used to calculate their fractal dimensions.

Fractal dimensions of these four types of pores from wells N1, N3, and N10 are presented in the form of box plots, and their total statistic number is 66, 61, and 63, respectively (Figure 8). DSP, DDP, DIP, and DMF not only decreased one by one but also showed a significant downward trend, with the main body between 2.60–2.80, 2.40–2.65, 2.20–2.40, and 2.05–2.30 (Figure 8). Fractal dimensions of the four types of pore surfaces in well N3 are relatively high, and N1 is close to N10 and relatively low. For example, the fractal dimension of intergranular pores and microfractures in well N3 is significantly higher than that in wells N1 and N10, which may be influenced by many factors.

Figure 8.

Figure 8

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Fractal dimensions of different types of pores calculated by SIA.

4.4. CH4 Gas Adsorption Analysis

CH4 gas adsorption isotherms could effectively characterize the shale gas adsorption capacity of samples under a certain temperature and pressure condition. Combined with the Langmuir equation, the CH4 adsorption capacity of eight samples from well N10 at 30 MPa and 75.5 °C was calculated (Table 2). The result shows that the CH4 adsorption capacity is between 0.6914 and 2.6333 cm3/g, with an average of 1.2670 cm3/g.

Table 2. Storage Capacity of Eight Shale Samples from Well N10 (under 30 MPa and 75.5 °C).

depth (m) 2111.20 2136.45 2152.34 2168.89 2183.24 2197.14 2213.22 2228.05
TOC (%) 1.76 1.33 1.28 1.21 1.45 2.24 2.44 4.28
adsorption capacity (cm3/g) 1.2434 0.8557 0.7998 0.6914 0.8636 1.5244 1.5244 2.6333
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5. Discussion

5.1. Relationship between Material Composition and Fractal Dimension

There is a positive correlation between D1 and TOC, and the R2 values of wells N1 and N10 are 0.3043 and 0.7246, respectively. When TOC is less than 4%, D1 shows an increasing trend with the increase of TOC. However, when it is more than 4%, its increase would not result in a further increase of D1 but would fluctuate around 2.60 (Figure 9a). It shows that the pore surface tends to be more complex and rougher with the increase of TOC, but when the TOC reaches a certain level, it will gradually become flat and will not increase further.

Figure 9.

Figure 9

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Fractal dimension (D1, D2) and its correlation with TOC and mineral composition. (a) Correlation between TOC and D1; (b) correlation between TOC and D2; (c) correlation between D1 and D2; (d) correlation between relative content of quartz and D1; (e) relationship between relative content of carbonate minerals and D1; (f) correlation between relative content of clay and D1; (g) correlation between relative content of quartz and D2; (h) relationship between relative content of carbonate minerals and D2; and (i) correlation between relative content of clay and D2.

Overall, there is a weak negative correlation between D2 and TOC, and with the increase of TOC, the pore structure tends to be relatively simple (Figure 9b). There is no correlation between D1 and D2, which indicates that the pore structure and pore surface are two different parameters and they have no definite relationship (Figure 9c). Relationships between D1, D2, and various minerals are relatively more complex and diverse (Figure 9d–i). For example, D1 and quartz content in N1 have a negative correlation, while they have a positive correlation in N10 (Figure 9d), which is consistent with previous studies.8,26,47−50 These results suggest that mineral composition has a complex and diverse effect on the pore system,45 and it should be further studied.

Specific surface area and specific pore volume are positively correlated with TOC (Figure 10a,b). This is because the increase of organic matter will significantly increase organic pores, which have large pore surface and pore volume.10−12,15,67 Because there are many inorganic pores in shale, the specific surface and specific pore volume are not controlled only by organic matter and organic pores.10,15D1 also has a positive correlation with specific surface area and specific pore volume,11,12,14 but R2 is smaller than that of TOC, specific surface area, and pore specific volume (Figure 10c,d). This is because of the comprehensive influence of various pore types, rather than a simple fractal dimension of organic pores, such as dissolution pores and organic pores. D2 has almost no correlation with specific surface area and specific pore volume (Figure 10e,f), and this is because it reflects the complexity of the pore structure.33,51,64

Figure 10.

Figure 10

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Relationship between specific surface area, specific pore volume, and fractal dimension. (a) Correlation with specific surface area and TOC; (b) correlation between specific pore volume and TOC; (c) correlation between D1 and specific surface area; (d) correlation between D1 and specific pore volume; (e) correlation between D2 and specific surface area; and (f) correlation between D2 and specific pore volume.

5.2. Relationship between the Fractal Dimension from N2-GA and SIA

D1 is the total surface fractal dimension of shale samples,33,45,51,68 influenced by the fractal dimension of different types of pores and their proportion, and it is a comprehensive reflection of fractal characteristics of the pore system. This study found that D1 has a good relationship with the fractal dimensions of the above four types of pores, that is, DDP > DOP > D1 > DI-P > DMF. Specifically, D1 is between DOP and DIP. It would be close to or equal to DOP when TOC increases, and close to DIP when TOC decreases (Figure 11).

Figure 11.

Figure 11

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Relevance of the fractal dimension obtained using FHH and SIA. (a) Well N1; (b) well N10.

Since dissolution pores and microfractures only account for a small proportion in the whole pore system, their control effect on D1 is relatively insignificant, and so organic pores and intergranular pores play a leading role. With the increase of TOC, the dominant role of organic pores becomes stronger and D1 increases accordingly. However, when TOC increases to a certain level, the upper limit of organic pores will be reflected, and so D1 will not increase indefinitely (Figure 9a). With TOC decreasing gradually, the dominant role of organic pores is weakened, and the influence of intergranular pores on the whole pore system is more prominent. Therefore, in samples with low TOC, D1 is relatively low and close to DIP. Similarly, D1 will not decrease indefinitely because of the lower limit of DIP.

Comparing these two methods, we could find that there is a significant difference between FHH and SIA. As mentioned above, the FHH model is based on N2-GA data to calculate the fractal dimension, and according to different adsorption behaviors under different pressure, the fractal dimension of the pore surface and pore structure would be obtained.26,33,51,63,64 SIA is based on two-dimensional images, and only pore surface parameters are used to deduce the fractal dimension of the three-dimensional pore surface. So, only the surface dimension of pores would be obtained.

5.3. Relationship between the Fractal Dimension and CH4 Adsorption Capacity

CH4 adsorption capacity shows a strong positive correlation with TOC (R2 = 0.9855), indicating that it is significantly affected by TOC.33,48,69,70 It has been confirmed that the increase of TOC can significantly increase the specific surface area (Figure 12a) of shale and greatly increase the adsorption points of CH4 molecules in shale, thus increasing CH4 adsorption capacity.27,48 In addition, previous studies on the heat of adsorption of CH4 molecules have shown that the adsorption rate of CH4 molecules on organic matter is higher than that on clay minerals, that is, the affinity of CH4 molecules on the surface of organic matter is stronger.71,72

Figure 12.

Figure 12

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Correlation between CH4 adsorption capacity, TOC, and fractal dimension. (a) Correlation between CH4 adsorption capacity, TOC, and D1; (b) correlation between shale CH4 adsorption capacity, TOC, and D2.

With the increase of TOC, the proportion of organic pores in the shale pore system would increase and lead to the increase in the surface fractal dimension D1 (Figure 11). Therefore, there is a positive correlation between D1 and CH4 adsorption capacity. As can be seen from Figure 12a, although the fractal dimension (D1) of N10 and CH4 adsorption data do not correspond one-to-one, they still have a significant positive correlation. Higher D1 means that shale has higher CH4 adsorption ability, which is consistent with previous results.33,48,70 Since D2 represents the complexity of the pore structure and has no direct influence on CH4 adsorption, there is no correlation between D2 and adsorption capacity (Figure 12b).

6. Conclusions

In this paper, gas adsorption experiments and Slit Island Analysis were used to study fractal dimension characteristics of pores and their influence on the CH4 adsorption capacity of marine shale in the southern Sichuan Basin, China. The following conclusions can be made:

  • (1)

    Organic pores, intergranular pores, dissolution pores, and microfractures are the most common reservoir spaces in shale, and their morphology, size, and content are greatly different. According to N2 adsorption isotherms, the hysteresis loops change from type H4 to type H2 with the increase of TOC, showing that samples with different TOC have a distinct difference in the pore structure.

  • (2)

    Based on N2 gas adsorption and the FHH equation, fractal dimension D1 of the pore surface and fractal dimension D2 of the pore structure were obtained, which are 2.32–2.66 and 2.82–2.88, respectively. D2 is larger than D1, indicating that the pore structure is more complex than the pore surface.

  • (3)

    According to SIA, DSP, DDP, DIP, and DMF were obtained with the main body of 2.60–2.80, 2.40–2.65, 2.20–2.40, and 2.05–2.30, respectively, indicating that the surface roughness of these kinds of reservoir spaces decreases gradually. Overall, DSP > DDP > D1 > DIP > DMF, and D1 is mainly affected by the content of organic pores, intergranular pores, and their fractal dimension. In rich TOC samples, as organic pores play a dominant role, DDP and D1 are close to each other, while in low TOC samples, D1 is close to DIP because the intergranular pores are dominant.

  • (4)

    Organic matter and organic pores are the key factors controlling the CH4 adsorption capacity of shale. The increase of TOC and organic pores could significantly improve CH4 adsorption capacity and at the same time increase the fractal dimension D1 of the shale pore system, which leads to a strong positive correlation between D1 and CH4 adsorption capacity. The fractal dimension D1 may be used as an effective parameter to characterize the CH4 adsorption capacity of shale, thus providing some evidence to further clarify the adsorption mechanism of shale gas.

Acknowledgments

This project was financially supported by the Innovation Consortium Project of China National Petroleum Corporation and Southwest Petroleum University (No. 2020CX020102), Natural Science Foundation of China (No. 1674211), and General Project of Chongqing Natural Science Foundation (No. cstc2021jcyj-msxmX0897).

Author Contributions

The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript.

The authors declare no competing financial interest.

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