Effect of coal facies on pore structure heterogeneity of coal measures: Quantitative characterization and comparative study

2.2.1 Experimental methods

The first step involved the microscopic identification of coal rock components based on the color, morphology, and structure of the coal samples. Then, the maceral analysis of the light section, prepared after crushing the coal seam, was carried out. The pulverized coal light sheet was examined under a reflective polarizing microscope using single polarization or incomplete orthogonal polarization. Accurate identification of macerals and minerals was achieved through quantitative analysis employing the number point method, as outlined in GB/T 8899 “Methods for Determination of Microscopic Components and Minerals of Coal.” Following this, the coal samples were ground into powdered form, and the vitrinite reflectance value (R _{o, max}) was measured using a microspectrophotometer. Finally, the coal samples were placed in a 40–60 mesh sieve to grind 6–10 g for subsequent analytical testing.

In this study, we focus on the pore characteristics (2–100 nm) of adsorption pores in coal reservoirs. According to the IUPAC pore classification method, pores with diameters of 0.4–2 nm are considered micropores, and pores with diameters of 2–100 nm are considered mesopores. The characterization of micropore structures involved the LPCO₂ GA test, whereas the LPN₂ GA test was employed for the characterization of mesopore structures.

2.2.2 Classification of coal facies

Various coal facies samples have been proposed in previous studies, forming the basis of classical coal facies research methods. Parameters, such as gelatinization index (GI), tissue preservation index (TPI), vegetation index (VI), groundwater index (GWI), vegetation index (VI), vitrinite/inertinite ratio (V/I), along with graphical analytical methods, such as TPI–GI phase diagrams and VI–GWI phase diagrams, have been popularly cited [23,24].

The more commonly cited methods for coal facies analysis include TPI, GI, VI, GWI, and GI–TPI phase diagram [25]. Upon the development and improvement of the calculation method, the formulae are as follows:

1. TPI = (telinite + colotelinite + semifusinite + fusinite)/(colodetrinte + macrinite + inertodetrinite)

2. GI = (vitrinite + macrinite)/(semifusinite + fusinite + inertodetrinite)

3. GWI = (gelinite + corpogelinite + minerals + vitrodetrinite)/(telinite + telocolinite + colodetrinite)

4. VI = (colotelinite + fusinite + semifusinite + suberinite + resinite)/(colodetrinite + inertodetrinite + alginite + liptodetrinite + sporinite + cutinite)

GI reflects the ratio of gelation products to non-gelation products. It can not only indicate the characteristics of water level changes in ancient peat bogs but also reflect the extent to which plant remains have been subjected to gelatinization. TPI represents the ratio of structural microscopic components to unstructured microscopic components in the vitrinite and inertinite, reflecting the degree of the well-preserved plant cell structure and the intensity of plant tissue degradation. GWI and VI signifies the degree of gelation of the fabrics depending on pH conditions [23,24].

2.2.3 Single-fractal model

The Frenkel–Halsey–Hill (FHH) model is the most widely used single-fractal model for analyzing liquid nitrogen test data [26]. Fractal values in this model are mainly obtained by linear fitting of adsorption and relative pressure. This fractal model can provide a detailed analysis of pore heterogeneity in the pore size range of 2–100 nm, with the fractal dimension calculated as follows:

Here, V is the adsorption volume corresponding to the equilibrium pressure P, cm³ g⁻¹; C is a constant; V ₀ is the adsorption volume of the monomolecular layer of gas, cm³ g⁻¹; P ₀ is the saturated vapor pressure, MPa; and A is the power law index, and its value is controlled by the fractal dimension (D), where a larger value of D indicates stronger pore heterogeneity.

Based on the CO₂ adsorption test results, the fractal model was used to study the heterogeneity of micropores. The equation can be expressed as

where S _r is the cumulative specific surface area, m² g⁻¹; r is the pore radius, nm; and D is the fractal dimension, dimensionless; surface fractal dimension D = 2 + C or D = (C – 3)/3. A larger D value indicates stronger heterogeneity of pores.

2.2.4 Multi-fractal model

Multiple fractal allows for a more detailed characterization of the complexity and heterogeneity of the sample. For reservoirs with strong heterogeneity, such as coal reservoirs, the pore size distribution curve will not only fluctuate but also jump randomly. In addition, different pore spacing parts are similar, making multifractals advantageous for calculating nanopore distribution heterogeneity [27,28]. Multifractal calculation results include two forms from previous studies, i.e., a∼f(a) singular and q∼D fractal dimension spectrum. It can be concluded that the two forms have an explicit correlation [29]. Therefore, in this study, the q∼D fractal dimension spectrum is selected to describe the multifractal results of coal samples. The formula is as follows:

where q is the index representing the fractal characteristics of objects at different scales. τ q is the q-order mass scale function and can be expressed as

Therefore, the generalized dimension (D _q ) can be defined as

When q = 1, D _q becomes

Relevant parameters include D _min, D _max, D ₀, D ₀ – D _max, and D _min – D ₀. Multifractal results calculated from the adsorption data show that in the low-value zone of pore volume, a larger D _min – D ₀ indicates a stronger heterogeneity in pore size distribution [30]. In the high-value zone of pore volume, increasing D ₀ – D _max indicates a stronger heterogeneity in pore size distribution.

3.2.1 Micropore distribution of samples with different coal facies types

The CO₂ adsorption curve reflects the pore size distribution of micropores. Figure 4a, c, and e show that the adsorption volumes of coal samples in coal facies A, B, and C are 5.77–12.15 cm³ g⁻¹, 6.64–13.35 cm³ g⁻¹, and 7.45–9.42 cm³ g⁻¹, respectively (Figure 4a, c, and e). The micropore distribution curves of all coal samples show two pore peaks at about 0.55 and 0.85 nm, respectively. The peak of the pore size distribution curves of coal facies B and C showed an inverted U-shape at 0.55 nm compared with that of coal facies A, which indicated that the pore size development is more homogeneous (Figure 4b, d, and f).

Figure 4

CO₂ adsorption curves of coal samples (a, c, e) and micropore distribution of different coal facies samples (b, d, f).

The volume and specific surface area of micropores are similar across three coal facies (Figure 5a and b), and also the pore volume percentage for the micropores of 0.40–0.55 nm, 0.55–0.85 nm, and 0.85–1.2 nm are similar among the three facies types (Figure 5c), showing that the coal facies types have little effect on the pore structures of micropores.

Figure 5

Comparison of structure parameters of micropores. Specific surface area of different coal facies types (a), pore volume of different coal facies types (b), and pore volume percentage of different coal facies types (c).

Although the pore size distribution curves show some differences across coal facies types, the peak pore size distribution is similar among the different coal types. Generally, micropores contribute the majority of pore volume (averaging 88%), followed by mesopores (averaging 8%), with macropores contributing the least pore volume (averaging 4%) (Figure 6a). The distribution characteristics of specific surface area also vary across coal facies types. Micropores typically provide most of the specific surface area (averaging 95%), with mesopores contributing around 5% and macropores contributing a negligible amount (Figure 6b). This indicates that micropores are well-developed in deep coal reservoirs. The pore volume and specific surface area distribution trends are consistent across different coal facies types, as the pore size range aligns with the development of the specific surface area. Moreover, micropores play a dominant role in contributing to both pore volume and specific surface area, suggesting that the primary sites for coalbed methane adsorption and storage are micropores with high specific surface areas, which also serve as effective pathways for initial gas migration and diffusion after desorption.

Figure 6

Distributions of the pores of different coal facies types: (a) the percentage of pore volume and (b) the percentage of specific surface area.

Previous studies have found that exinite and inertinite contain fewer pores, whereas pores are well-developed in vitrinite, and the abundance of mineral pores is related to the types of minerals present in coal. Coal facies A is characterized by a high vitrinite content with well-developed micropores and relatively low permeability, whereas coal facies C, characterized by high inertinite content, exhibits more meso- to macropores and higher permeability (Figure 7a and b). Compared to inertinite, vitrinite shows a positive correlation with micropore volume, indicating that vitrinite plays a role in controlling micropore development (Figure 7c and d).

Figure 7

Vitrinite and inertinite content of different samples (a), permeability data (b), and the relationship between micropore volume and submicroscopic components (c and d).

Figure 8 shows a strong positive correlation between R _o,max of micropores, and both pore volume and specific surface area. As R _o,max increases, the pore volume of each sample increases linearly, accompanied by an increase in specific surface area. This is primarily due to an increase in coal maturity, where macropores gradually decrease while micropores, such as adsorption pores, increase. The R _o,max values for all samples range from 0.65 to 2%, classifying them as medium-rank coal. However, there are differences in R _o,max values across different coal facies types: coal facies A has the highest average R _o,max (average 1.23%). The samples from coal facies A also show the largest pore volume and specific surface area, consistent with the higher vitrinite content characteristic of this facies.

Figure 8

Relationship between micropore volume and R _{o, max.}. Crossplots of R _{o, max.} and pore volume (a) and crossplots of R _{o, max.} and specific surface area (b).

3.2.2 Single-fractal analysis based on carbon dioxide adsorption curves

The micropore fractal characteristics are analyzed using the CO₂ adsorption data (Figure 9). The results indicate that there exist differences in the two segments of the single-fractal curve of micropores before and after the critical diameter, taken as 0.6 nm. This division illustrates the heterogeneity of the pore distribution for pores smaller than 0.4–0.6 nm and 0.6–2.0 nm.

Figure 9

Fractal curves of micropore distribution. Single fractal curves of coal facies A (a), single fractal curves of coal facies B (b), and single fractal curves of coal facies C (c).

The demarcation point of the fractal curve is approximately ln (r) = −0.5 (r = 0.60 nm), indicating significantly different fractal characteristics (Figure 9). Calculations confirm that this value corresponds to the position of peak 1 in Figure 4b, d, and f. Therefore, the fractal demarcation point is determined to be the average peak position of 0.60 nm. The fractal dimension for each sample comprises two parameters, namely D _s1 (r < 0.6 nm) and D _s2 (r > 0.6 nm). The results show that D _s1 ranges from 1.76 to 5.3 (Figure 10a), which falls outside the typical fractal range of D between 2 and 3 [30,31,32]. This deviation is primarily attributed to the limited pore data points in the range of 0.47–0.60 nm during the testing process, resulting in a calculation range of only 0.13 nm. To ensure accurate calculations, this section focuses in terms of fractals only on micropores larger than 0.60 nm.

Figure 10

D _S1 of different coal facies types (a) and D _S2 of different coal facies types (b).

The calculated D _s2 values range from 2.77 to 2.95, demonstrating clear fractal characteristics. The D _s2 values for coal facies A, B, and C are 2.77–2.95, 2.84–2.86, and 2.83–2.86, respectively (Figure 10b). The D _s2 values exhibit minimal variation among different coal facies types, indicating that coal facies has a limited effect on micropore development, a conclusion supported by Figure 5. However, the D _s2 values of coal facies A (2.77–2.95) are larger than those of other types, suggesting that the samples in coal facies A have the strongest heterogeneity in the 0.6–1.2 nm pore distribution range.

3.2.3 Multi-fractal analysis based on CO₂ adsorption curves

The single fractal cannot fully characterize the heterogeneity differences of micropores. In this article, the q ∼ D fractal dimension spectrum is selected to describe the multifractal results. Taking the sample M-2 as an example, the relationship between lg(x(q, ε)) and lg(ε) was studied (Figure 11a). There is a good linear relationship between q and i(q) (Figure 11b), and as q increases i(q) increases monotonically, illustrating multi-fractal behavior in micropore size distribution. Significant differences in D ₀ – D ₁₀ and D ₋₁₀ – D ₀ among all samples indicate substantial variations in pore volumes within the micropore range (Figure 11c, d, and f). D ₀ – D ₁₀ exhibits less variation among all samples, whereas D ₋₁₀ – D ₀ displays more variability among different coal facies types. Specifically, D ₋₁₀ – D ₀ for coal facies A, B, and C ranges from 0.1 to 0.22, 0.09 to 0.16, and 0.12 to 0.18, respectively.

Figure 11

Multifractal curves characteristics of micropores. The linear relationship between q and i(q) (a, b), and the linear relationship between q and D(q) in different coal facies types (c–e).

D ₋₁₀ (1.13–1.15) and D ₁₀ (0.97–0.98) exhibit less variation among all samples (Figure 12a and b). The values of D ₋₁₀ – D ₀ and D ₀ – D ₁₀ are larger for coal facies A compared to other types, suggesting stronger heterogeneity in micropore distribution in both the low- and high-pore-volume development areas of this coal facies (Figure 12c and d). D ₋₁₀ – D ₁₀ of coal facies A is 1.1–1.22 (Figure 12e), surpassing other types, further emphasizing the stronger heterogeneity in micropore distribution for coal facies A.

Figure 12

Comparison of multi-fractal characteristics between different coal facies types. D ₁₀ and D _‒10 of different coal facies types (a, b), the relationship between D ₁₀, D _‒10 and D ₀ (c–e).

As D ₋₁₀ – D ₀ increases, D ₋₁₀ – D ₁₀ increases linearly with an R ² of 0.98, and D ₀ – D ₁₀ increases similarly (Figure 13a), indicating that the lower pore volume area controls the heterogeneity of the micropore size distribution. The volume percentage of pores smaller than 0.55 nm increases progressively with D ₋₁₀ – D ₀, and the heterogeneity of the micropore size distribution is impacted by pores smaller than 0.55 nm.

Figure 13

Relationship between multi-fractal and pore structure parameters. Plots of D _‒10 – D ₁₀ and D ₀ – D ₁₀ (a), the relationship between D _‒10 – D ₀ and pore structure parameters (b).

3.3.1 Mesopore distribution of samples of different coal facies types

The N₂ adsorption curve reflects the pore size distribution of mesopores. The total adsorption volume for coal facies A ranges from 0.71 to 8.64 cm³ g⁻¹, and that for coal facies C is 0.56–0.89 cm³ g⁻¹ (Figure 14a, c and e). Coal facies A exhibits separated adsorption–desorption curves with clear hysteresis loops (except for sample M-2), suggesting the development of ink-bottle pores with a more complex pore structure. Conversely, coal facies C displays coinciding adsorption–desorption curves, indicating well-developed open pores are a simpler pore structure. Coal facies B, represented by varying adsorption and desorption curve morphologies, shows obvious hysteresis loops and ink-bottle pores in samples H-2 and H-3, while samples M-5 and M-8 display open pores. Coal facies B samples are in a transitional stage between coal facies A and C, exhibiting relatively complex variations (Figure 14a, c, and e). Two peaks are shown in mesopore distribution curves at about 10 nm and 45 nm (Figure 14b, d, and f).

Figure 14

N₂ adsorption curves of coal samples (a, c, e) and mesopore size distribution of different coal facies samples (b, d, f).

The pore volume and specific surface area of mesopores are the largest for coal facies A (0.007 cm³ g⁻¹ and 2.5 m² g⁻¹), indicating the most developed mesopores in coal facies A (Figure 15a and b). The percentage of pore volume with a diameter of 2–10 nm in coal facies A is the lowest among the three coal facies, whereas the volume percentage of 10–50 nm pores in coal facies A is much higher than that of other coal facies (Figure 15c). These results underscore the influence of coal facies type on mesoporous structure development.

Figure 15

Comparison of mesopore structural parameters among different coal facies samples. Specific surface area of different coal facies types (a), pore volume of different coal facies types (b), and pore volume percentage of different coal facies types (c).

Compared to micropores (Figure 8), the pore volume and specific surface area of 2–100 nm pores show a weaker correlation with R _o,max (Figure 16). It is suggested that the pore structure within this range is influenced not only by coal maturity but also by fundamental coal parameters such as moisture and ash content, making the structural variations of these pores more complex than those of micropores.

Figure 16

Relationship between mesopore volume and R _{o, max}. Crossplots of R _{o, max} and pore volume (a, c) and crossplots of R _{o, max} and specific surface area (b, d).

The specific surface area of 2–50 nm and 50–100 nm pores shows a weak correlation with vitrinite content (Figure 17a and c), while a certain correlation exists with inertinite content. As inertinite content increases, the specific surface area of the pores decreases (Figure 17b and d). Compared to coal facies A, coal facies B and C have higher inertinite content, fewer micropores, poorer adsorption capacity, and more developed mesopores and macropores, resulting in higher permeability. This indicates that inertinite plays a controlling role in coal reservoirs where meso- and macropores are predominant.

Figure 17

Relationship between mesopore-specific surface area and vitrinite (a, c), and relationship between mesopore-specific surface area and inertinite (b, d).

3.3.2 Single-fractal analysis based on N₂ adsorption and desorption curves

The N₂ adsorption curve is employed to examine the mesopore fractal dimension, with limited studies conducted on the fractal dimension of the desorption curve. It was found that the fractal values obtained by the liquid nitrogen desorption curve are also physically meaningful [33]. Utilizing the FHH model, all coal samples are subjected to a single fractal, and the fractal dimension is calculated (Figure 18). Figure 18 shows that the two sections of the fractal curves are roughly circumscribed by P/P ₀ = 0.5, which corresponds to a pore size of 4 nm.

Figure 18

Fractal curves of mesopores using N₂ adsorption desorption data (a, c, e) and N₂ desorption data (b, d, f).

The single fractal dimension contains four parameters in each coal sample, i.e., D ₁ (P/P ₀ < 0.5, in the adsorption curve), D ₂ (P/P ₀ > 0.5, in the adsorption curve), D ₃ (P/P ₀ > 0.5, in the desorption curve), and D ₄ (P/P ₀ < 0.5, in the desorption curve). The fractal dimension values are the following: D ₁ = 2.05–2.71, D ₂ = 2.37–2.66, D ₃ = 2.57–2.76, and D ₄ = 2.25–2.69. These values fall within the defined fractal range of 2–3, indicating clear fractal characteristics across the entire pressure range.

Previous research has demonstrated that the fractal dimension value obtained by P/P ₀ < 0.5 represents the heterogeneity of pore volume and reflects the pore space morphology [34]. Similarly, values obtained for P/P ₀ > 0.5 also represent the heterogeneity of pore surface area and reflect the pore surface morphology. Compared to coal facies B and C, the fractal curves of coal facies A are nearly straight lines, indicating consistent heterogeneity in the mesopore distribution of coal facies A samples (Figure 18a, c, and e). The fractal slopes obtained from the desorption curves range between −0.75 and −0.25, indicating fractal significance (Figure 18b, d, and f). The four parameters of coal facies A are larger than those of the other two coal facies, which indicates that the heterogeneity of mesopore restricted by coal facies A is the strongest (Figure 19).

Figure 19

D ₁ values of different coal facies types (a), D ₂ values of different coal facies types (b), D ₃ values of different coal facies types (c), D ₄ values of different coal facies types (d).

A linear positive correlation exists between D ₁ and D ₃ (R ² = 0.73), indicating that the liquid nitrogen desorption curve conforms to the fractal condition and exhibits fractal significance (Figure 20a). Additionally, D ₁ and the volume percentage of pores with 10–50 nm have a linearly positive association. (Figure 20b), indicating that the mesopore distribution heterogeneity is regulated by pores of 10–50 nm. This also indicates that D ₁ reflects the volume roughness of the pore structure, aligning with previous experimental observations [35].

Figure 20

Multi-fractal dimension correlation. The relationship between D ₁ and D ₃ (a), relationship between D ₁ and pore volume percentage (b).

3.3.3 Multi-fractal analysis based on N₂ adsorption and desorption curves

Taking the sample M-1 as an example, the relationship between lg(x(q, ε)) and lg(ε) was studied. When q < 0, i(q) increases with an increase of q, while when q > 0, the increase of i(q) is not obvious (Figure 21b). This pattern suggests a multi-fractal behavior in mesopore size distribution. D ₀ – D ₁₀ and D ₋₁₀ – D ₀ showed significant differences across all samples, indicating substantial variations in mesopore volumes. D ₋₁₀ – D ₀ varies more among different coal facies, with D ₋₁₀ – D ₀ values for coal facies A, B, and C ranging from 0.34 to 0.94, 0.39 to 0.74, and 0.47–0.83, respectively (Figure 21c, d and f).

Figure 21

Multifractal curves characteristics of mesopores. The linear relationship between q and i(q) (a, b), and the linear relationship between q and D(q) in different coal facies types (c–e).

In the low-value zone of pore volume, a larger D _min – D ₀ indicates stronger heterogeneity. In addition, in the high-value zone, increasing D ₀ – D ₁₀ indicates stronger heterogeneity in pore size distribution. D ₁₀ (0.085–0.105) for the coal facies types show minimal differences, with the D ₋₁₀ of coal facies A higher than that of coal facies B and C (Figure 22a and b). These results suggest that the mesopore distribution in coal facies B and C is more homogeneous compared to coal facies A. The D ₋₁₀ – D ₀ and D ₀ – D ₁₀ of coal facies A are the largest compared to coal facies B and C, suggesting that coal facies A is more heterogeneous in the pore-volume low-value zone and the pore volume of the high-value zone (Figure 22c and d). Figure 22e shows that the D ₋₁₀ – D ₁₀ of coal facies A is 2–8 (larger than other types), indicating an overall stronger heterogeneity of mesopore distribution.

Figure 22

Comparison of multi-fractal parameters in different coal facies types. D ₁₀ and D _‒10 of different coal facies types (a, b), the relationship between D ₁₀, D _‒10 and D ₀ (c–e).

As D ₋₁₀ – D ₀ increases, D ₋₁₀ – D ₁₀ increases linearly with an R ² of 0.99 (Figure 23a), indicating that the heterogeneity of the mesopore distribution is primarily governed by the lower pore volume area. Furthermore, D ₋₁₀ – D ₀ gradually increases with an increase in the volume percentage of pores of 10–50 nm, indicating that pores of 10–50 nm play a significant role in governing the heterogeneity of mesopores.

Figure 23

Correlation between multi-fractal parameters. Plots of D _‒10 – D ₁₀ and D ₀ – D ₁₀ (a), the relationship between D _‒10 – D ₀ and pore structure parameters (b).