Eight coal samples were collected in representative coalfields in China, their ranks ranging from low metamorphic lignite to high metamorphic anthracite. Samples GS (lignite) and SGT (bituminous C) were taken from Pingzhuang Coalfield and Dongsheng Coalfield in Inner Mongolia Province respectively. Sample XZY (bituminous C) was obtained from Datong Coalfield in Shanxi Province. These coal seams belong to the Jurassic coals. Sample TS (bituminous B) was collected from Kailuan coalfield in Hebei Province. Sample ZB (bituminous B) was obtained from the Huoxi coalfield in Shanxi Province. Samples ZC (bituminous A), YW (bituminous A) and NY (anthracite) were obtained from the Qinshui coalfield in Shanxi Province. These five coal samples belong to the Carboniferous-Permian coals. Fresh coal samples were gathered carefully from mining working faces. Then, samples were vacuum-sealed and immediately brought to test in the laboratory.

Block samples were broken into smaller piece samples with a hammer in the laboratory. A sample of each coal with a diameter larger than 1 cm was selected and polished into a slice sample with ∼1 cm diameter and ∼1 mm thickness with sandpaper. The prepared slice samples were used for SAXS experimental study. Furthermore, crushed coal samples with small particles were collected and ground. After pulverization, particle samples of 60–80 mesh were selected for low-temperature nitrogen adsorption experiments and subsequent analyses.

Based on Chinese national standards GB/T 30,732–2014, the proximate analyses of coal samples were performed by using the automatic analyzer. Vitrinite reflectance measurements were conducted on polished coal samples employing a Leitz MPV-3 photometer microscope in accordance with Chinese national standards GB/T 6948–2008. The proximate analyse and maximum vitrinite reflectance results are listed in Table 1. The ultimate analyses of coal samples were performed according to Chinese national standards GB/T 31391–2015. The automatic true density analyzer was used to test the true relative density of coal samples. The results are presented in Table 2.

The SAXS experiments were conducted at the 1W2A line station of Beijing Synchrotron Radiation Facility (BSRF) (Li et al., 2014). The incident monochromatic X-ray beam was provided with energy fixed at 8.052 keV and its wavelength is fixed at 0.154 nm. The focused X-ray spot size is about 1.4 mm (horizontal) × 0.2 mm (vertical). The detectable region of scattering vector ( q = 4 π ⁡ sin ⁡ θ / λ ) is mainly determined by the length of the SAXS camera for detector. In this experiment, the distance between sample and detector was 1,570 mm, and the measured scattering vector (q) ranges from 0.097 to 3.339 nm⁻¹.

The sample holder with a cavity of 10 mm in diameter and 1 mm thickness was used to place test sample. The prepared circular slice samples were put into the cavity and fixed for SAXS experiment. This experiment was conducted in the air environment, and the air background was subtracted in subsequent data processing. To calculate pore structural parameters, the absolute scattering intensity is necessary (Xie et al., 2018). In this study, the absolute scattering intensity was calibrated by using the glassy carbon SRM 3600 (Xie et al., 2018).

The mass of each sample was weighed prior to SAXS experiment in order to compare the differences in pore structure for samples with a same mass standard. The results are presented in Table 3.

The porosity of porous materials can be calculated from the invariant Q_inv as Eq. 1 (Radlinski, 2006; Xie et al., 2018): Q i n v = ∫ 0 ∞ q 2 ( ∂ Σ ∂ Ω ) s ( q ) d q = 2 π 2 ( Δ ρ e ⋅ r e ) 2 P ( 1 − P ) (1) where, q is the scattering vector (nm⁻¹), ( ∂ Σ ∂ Ω ) s ( q ) is the absolute scattering intensity (cm⁻¹), Δ ρ e is the electron density difference between solid matrix and pore in the material (e/ų), r e is the classical electron radius which is equal to 2.8179 × 10⁻¹³ cm, and P is the porosity (%).

Coal is considered to be a two-phase polydisperse system composed of coal matrix and pores (Radlinski et al., 2004). The electron density of pores in coal approximates zero. Therefore, the electron density difference Δ ρ e between the coal matrix and the pores is about the electron density of coal matrix.

The electron density of coal matrix can be calculated by the true relative density and ultimate analyses results as Eq. 2 (Radlinski, 2006): ρ e = ρ N A ∑ α i Z i ∑ α i M i (2) where, ρ is true relative density, N_A = 6.022 × 10²³ is Avogadro’s number, i represents a kind of element, α_i is the content with percent of element i, Z_i is the number of electrons of element i, M_i is the molecular weight of element i.

The real space size of a scatterer is shown in Eq. 3 (Li et al., 2018): 2 π q max ≤ d ≤ 2 π q min (3) where, q is the scattering intensity (nm⁻¹) and d is the pore diameter (nm). The measured scattering vector (q) ranges from 0.097 to 3.339 nm⁻¹ in this experiment, so the pore diameter of each sample characterized were approximately 2–65 nm. Detailed information on processing SAXS experimental data was provided in our previous publication (Zhao et al., 2020).

Low-temperature nitrogen adsorption experiments were performed on an ASAP 2020Plus surface area and porosity analyzer (Micromeritics, United States). According to China’s national standard GB/T 21650.2-2008, the test was conducted by using the static volumetric method. Samples prepared from 60 to 80 mesh particles were selected for the LTNA experiment.

Prior to analysis, 1.0 g of each coal sample was degassed under vacuum at 110°C for approximately 10 h, then the degassed sample was weighed again. Afterward, the test tube was connected to the experimental instrument for analysis. An appropriate amount of high-purity liquid nitrogen (purity >99.999%) was put into the Dewar flask to provide the low-temperature of liquid nitrogen (77 K) for this experiment.

Both adsorption and desorption isotherms were tested at the relative pressure (P/P₀) in the range of 0.01–0.995 (P is the equilibrium pressure and P₀ is the saturated vapor pressure at the temperature of liquid nitrogen, approximately 0.1013 MPa). The equilibrium state during entire experimental process was controlled automatically. Then, the isotherms of adsorption and desorption were obtained. Finally, the pore structure parameters of samples were acquired by the instrumental software.

The scattering curves for eight coal samples with different ranks are presented in Figure 1. The overall trends are similar in the scattering curves for samples, and the scattering intensity I of the samples decrease with scattering vector q increasing. Over the entire scattering vector range of 0.097–3.339 nm⁻¹, sample NY and sample YW exhibit high scattering intensity I, while sample ZB has the lowest scattering intensity I, and the scattering intensity I of other samples are between it of samples NY and ZB. For most samples, when the scattering vector q is 1 nm⁻¹, the scattering intensity I decreases to a low value. When the scattering vector q is larger than 1 nm⁻¹, the scattering intensity I basically remains stable or decreased slightly. The scattering curves for different samples reflect the differences in nanopores structure, which may be mainly related to the different ranks of coal samples (Zhao et al., 2014).

When processing SAXS data, it is necessary to calibrate the initial experimental data based on Porod’s theory. In this study, the original Porod’s curve of each sample shows obvious positive deviation effects. This is due to the existence of non-uniform regions of nano-scale electron density in the sample (Li, 2013). The electron density of coal matrix fluctuates slightly because of heterogeneity of coal matrix and presence of mineral matter (Zhao et al., 2020). To obtain the structure of pores in coal, the deviation correction is essential. The Porod’s curve deviation correction for sample (GS sample as an example) was shown in Figure 2. The corrected SAXS data was used for subsequent processing and analysis.

The porosity of each sample was quantified by using the absolute scattering intensity. In this paper, the X-ray beam size was 1.4 × 0.2 mm². The thickness of the sample is 1 mm. Combined with the sample volume and mass in the beam testing area, the porosity was then normalized to mass weighted pore volume for each sample, as presented in Table 4. Variation in pore volume of samples with coal rank is shown in Figure 3.

With changes in the metamorphic degrees of coals, the overall pore volume of coal first increased, then decreased, then increased and decreased as shown in Figure 3. The pore volume of sample GS (lignite) with the lowest degree of metamorphism is 17.587 mm³/g, and that of sample SGT (bituminous C) is 22.654 mm³/g. A decreasing trend in the pore volume is observed from sample SGT (bituminous C) to sample ZB (bituminous B). The pore volume of sample ZB (bituminous B) is 9.996 mm³/g, the smallest pore volume among the eight coal samples. For coals with higher metamorphism degree, the pore volume of sample YW (bituminous A) is 25.334 mm³/g, which is the largest pore volume among the eight coal samples. For sample NY (anthracite), the pore volume is slightly lower at 23.015 mm³/g.

Coal is considered to be a two-phase polydisperse system composed of coal matrix and pores (Radlinski et al., 2004; Bahadur et al., 2015). In this study, the international software McSAS was used to investigate the pore distribution characteristics of each coal sample (Bressler et al., 2015). The SAXS data was analyzed using polydisperse sphere model, and the pore size distribution obtained was just a relative volume fraction. By combining this result with the pore volume per unit mass for each sample, the pore size distribution normalized to the mass weighted pore volume was obtained. The pore size distributions of various samples are presented in Figure 4. Within the range of 2–65 nm, all coal samples exhibit pore size distribution, but there are distribution differences among them. For pores with diameter less than 20 nm, samples SGT (bituminous C), XZY (bituminous C), YW (bituminous A), NY (anthracite) have larger pore volume, indicating that these four coal samples have more pores within this pore size range. For pores with the diameter larger than 20 nm, except for sample ZB (bituminous B), the pore size distributions of the other coal samples have no obvious difference. The pore volume of sample ZB (bituminous B) is small over the entire pore size distribution range, indicating that ZB (bituminous B) has few nanopores within the range of 2–65 nm.

The physisorption isotherms were classified into eight types by IUPAC (Thommes et al., 2015). The low-temperature N₂ adsorption isotherms of the eight coals with different ranks are presented in Figure 5. The isotherms of samples are closer to a combination of type II and type IV(a) isotherms, indicating that coals have complex pore structure. On the whole, the adsorption process for coal samples can be divided into micropore filling, monolayer adsorption, multilayer adsorption and capillary condensation (Choi et al., 2001; Sing and Williams, 2005). At extremely low relative pressures (P/P₀ < 0.1), the nitrogen quantity adsorbed increases obviously because nitrogen molecules fill micropores with pore size close to the diameter of gas molecules. Physisorption in mesopores and macropores is distinct from that in micropores. With increasing relative pressure, nitrogen molecules are gradually adsorbed onto surfaces of mesopores in coals, which is monolayer adsorption. Then, the adsorption isotherm is relatively flat (P/P₀ < 0.4). In this process, multi-layer nitrogen molecules are adsorbed on pore surfaces in coals. When the relative pressure exceeds 0.4, with continuous multilayer adsorption, an increasing number of nitrogen molecules undergo capillary condensation in the pores of coal (Hou et al., 2017). The nitrogen condenses to a liquid-like phase, and the amount of nitrogen adsorbed increases obviously.

Figure 5 shows that the types of hysteresis loops of physisorption isotherms for the eight coal samples are not consistent. Among them, the adsorption and desorption curves of some coal samples are close to overlapping, while physisorption isotherms of some coal samples have obvious hysteresis loops. Based on the latest classification of hysteresis loops from IUPAC (Thommes et al., 2015), the hysteresis loops for the eight coal samples can be divided into three types. The hysteresis loops of sample GS (lignite) and sample TS (bituminous B) belong to the same type, and the hysteresis loops are inconspicuous, which indicates that their pore morphology is mainly slit-like and plate-like with one side closed (Zhao et al., 2016). The isotherms of samples XZY (bituminous A), ZB (bituminous B), ZC (bituminous C), and YW (bituminous C) show small adsorption hysteresis loops, corresponding to type H4. This means that the pores in these coals are mainly cylinder-like and cone-like, and they are open on both sides with good connectivity (Chen et al., 2017). The physisorption isotherms of samples SGT (bituminous A) and NY (anthracite) have obvious hysteresis loops, corresponding to type H2. Their desorption curves drop sharply when the relative pressure is less than 0.5, demonstrating that both coals have “ink-bottle” pores (He et al., 2020).

The pore size distribution can be obtained for each sample using the nitrogen adsorption curves of samples and BJH theory (as shown in Figure 6). Samples other than NY exhibit pores with diameter less than 10 nm, and these contributed various pore volume. In the range of pore diameter less than 10 nm, samples GS, SGT and XZY show the largest pore volume for the pores with approximately 10 nm diameter, while samples TS, ZB, ZC and YW show the largest pore volume for pores with diameter of approximately 2 nm. Sample NY has few pores with diameter less than 10 nm. For pores with diameter greater than 10 nm, the pore volume of all eight coal samples increases with an increase in pore diameter.

Using BJH theory, the pore volume was obtained for pores with diameter less than 65 nm in coal samples with different ranks, and this is considered to be the open pore volume of coal. By combining the LTNA experimental results with the previous SAXS results, the characteristics of open and closed pores within the range of 2–65 nm can be determined for each sample. The results of pore volume and open/closed porosity measured by the two kinds of experiments are shown in Table 5.

To compare the pore volume determined by LTNA and SAXS experiments for coals with different ranks, two experimental results of each coal are compared by histogram, as shown in Figure 7. According to the SAXS results, the pore volume of samples decreases in the order YW > NY > SGT > XZY > GS > ZC > TS > ZB. According to the LTNA results, the order decreases as SGT > YW > GS > XZY > ZC > NY > TS > ZB. The orders of pore volume differ for the two experiments. The SAXS results show that the pore volume of YW is the largest, but the pore volume of SGT is the largest in the LTNA experiment. Moreover, the pore volume of NY is the second among the eight coal samples according to SAXS results, while its pore volume ranks sixth among the eight coal samples based on LTNA results. The difference in the orders of pore volume for the two experimental techniques reveals the difference in open and closed porosity in coals with different ranks.

In the LTNA experiments, open pores in the target range can be detected by nitrogen adsorption, while total pores information (including open pores and closed pores) in the target range can be measured by SAXS experiment. A combination of the two experimental methods effectively detects the open porosity and closed porosity within the target range for the sample, thereby evaluating the characteristics of open pores and closed pores for sample. The results indicate that the open porosity of sample SGT is the highest at 60.81% and that of GS is also high at 57.41%, while the open porosity of medium-metamorphic coals (samples XZY, TS, ZB, ZC) is approximately 50%. The open porosity of sample YW is 43.17% and that of NY is the lowest among the eight samples at 32.54%. On the whole, the open porosity of low-metamorphic coals is relatively higher, the open porosity of medium-metamorphic coals is in the middle, and the open porosity of high-metamorphic coals is relatively lower. Accordingly, the closed porosity of coals shows the opposite trend.

Figure 8 shows the variation in closed porosity of samples with coal ranks. The figure was divided into three parts: low-metamorphic coals (GS and SGT); medium-metamorphic coals (XZY, TS, ZB, ZC) and high-metamorphic coals (YW and NY). Fitting the closed porosity of the three parts basically shows that the closed porosity increases from low-metamorphic coals to medium-metamorphic coals, the closed porosity of medium-metamorphic coals increases slightly with the increase of coal rank, and the closed porosity of high-metamorphic coal increases significantly with the increase of coal rank. This may be related to the different molecular structure of coals with different ranks (Liu et al., 2019; Ren et al., 2021).

For low-metamorphic coals, the molecules contain more irregular parts, such as aliphatic chains and functional groups, while there are few aromatic rings (Yan et al., 2020a). The gaps between them often form large pores, and the macroscopic structure of coals is loose (Jiang et al., 2019b). Because there are a great number of chain structures in low-metamorphic coals, their overall molecular structure arrangement is disordered and spaced. It is easier for side chains, bridge bonds and functional groups to form connected pores with each other. Therefore, there are many connected pores in low-metamorphic coals, and the extent of their closed porosity is low. For medium-metamorphic coals, most of the alkyl side chains and functional groups have fallen off (Yan et al., 2020b). At the same time, aromatization has led to more aromatic rings structure and the intermolecular arrangement has become relatively dense (Jiang et al., 2019a). Due to the losses of side chains and functional groups, aromatic rings are typically connected by bridge bonds, which reduces the opportunity to form connected pores. In addition, aromatization converts the aliphatic chain structures into closed aromatic rings, which may also reduce the open porosity and increase the closed porosity of medium-metamorphic coals. For high-metamorphic coals, the mechanism for molecular evolution is mainly polycondensation, and irregular parts such as functional groups and side chains have basically disappeared (Meng et al., 2020). The degree of condensation for aromatic rings in coal macromolecules has improved continuously. The aromatic units extend horizontally and stack vertically, which obviously improves the order and density of the corresponding macromolecular structure (Niu et al., 2019). The dense arrangement of the molecular structure provides for easy formation of closed pores between aromatic rings in high-metamorphic coals. Therefore, the closed porosity in high-metamorphic coal is significantly increased.

Previous studies have shown that when selecting powdered samples for LTNA experiments, the number of open pores in coal is increased during the pulverization process (Jin et al., 2016; Si et al., 2017). The quantity of nitrogen adsorbed by samples with small particle sizes in the LTNA experiment is greater, and the corresponding open pore volume is larger. Our previous research shows that pulverization also increases the total pores (both open and closed pores) volume in coal (Zhao et al., 2020). In this paper, slice samples similar to the original state of coal were selected for SAXS experiment, and 60–80 mesh particle samples were selected for LTNA experiment. This may increase the open pore volume obtained from LTNA experiment relative to that of the original sample. Therefore, the open porosity values obtained in this study may be larger than the open porosity present in the original state of coal, and the corresponding closed porosity may be smaller. The actual closed porosity in coal may be greater than those determined experimentally in this paper.