Evolution of pore characteristics and methane adsorption characteristics of Nanshan 1/3 coking coal under different stresses

To ascertain the evolution of pore characteristics and methane adsorption characteristics of the unit cell of Nanshan 1/3 coking coal under different stresses, proximate analysis, ultimate analysis, solid-state 13C nuclear magnetic resonance spectroscopy (13C-NMR) and X-ray photoelectron spectroscopy (XPS) experiments were performed on the coal samples, and a molecular unit cell model of 1/3 coking coal was established. As the increase of stress, pore diameter, proportion of larger pores, number of pores, surface area, and pore volume all decrease, the rate of decrease gradually decreases, and the smaller pores are less affected. Under 8 kinds of stress, the methane adsorption capacity and the overall system energies all conform to the Langmuir adsorption curve; as the stress increases, the methane adsorption capacity and the overall system energies both decrease, the rate of decrease gradually decreases, and the order of the adsorbed methane increases. Stress changes the methane adsorption capacity by changing the pore characteristics of the unit cell, and the stress has a more obvious effect on larger pores. As the stress increases, the speed of the stress's influence on the pores weakens. This has certain guiding significance for studying the saturated adsorption capacity of methane under different original in-situ stresses.

www.nature.com/scientificreports/ temperature inhibit coal gas adsorption. Zhang et al. 35 studied the influence of micropore parameters and oxygenic functional groups on the adsorption capacity of methane. Wang and Pan et al. 36,37 studied the influence of temperature, pressure and moisture content on the adsorption capacity of methane. Mosher, Liu and Wang et al. [38][39][40] studied the effect of pore size and pressure on the methane adsorption capacity of coal. Nie, Chen, Zhao and Liu et al. [41][42][43][44] studied the influence of pore structure characteristics on coal's gas adsorption capacity through simulation and experiment. Shan and Yeganegi et al. 45,46 studied the influence of pore shape on the gas adsorption capacity of coal. Liu et al. 47 studied the influence of pressure and moisture content on the gas adsorption capacity of coal. Dang et al. 48 studied the influence of functional groups, pressure and electrostatic on the gas adsorption capacity of coal.
Based on the above literature analysis, the research on methane adsorption characteristics of coal seam under three-dimensional stress is insufficient. Based on the experiment, the molecular model of Nanshan 1/3 coking coal is established, this article comprehensively analyzes the evolution of the pore characteristic parameters of the unit cell model and the adsorption characteristics of methane under different stress conditions (the six sides of the unit cell are subjected to the same stress).The research has a certain guiding significance for the evolution of coal pore characteristics and the saturated adsorption capacity of methane under different in-situ stress conditions.

Coking coal molecular model construction
Coal sample test results. Proximate analysis, ultimate analysis, 13 C-NMR and XPS tests were performed on Nanshan 1/3 coking coal. The methods refer to literature [49][50][51] . The results of proximate analysis and ultimate analysis are shown in Table 1.
For the peak fitting of the 13 C-NMR spectrum, the structure attribution of the carbon element is judged according to the chemical shift value [52][53][54][55][56][57] , and the peak fitting is shown in Fig. 1. According to the relative area value of each structure, the 13 C-NMR structural parameters of the coal sample were calculated, as shown in Table 2.
According to the structure parameter value, calculate the ratio of aromatic bridge carbon to perimeter carbon, X BP , as shown in Eq. (1) 58 .
(1)   www.nature.com/scientificreports/ The Avantage software was used to perform peak fitting of heteroatoms (C, O, N) in XPS 59 , ignoring the lower content of S 60 , and judge the structure attribution of C, O, N elements based on chemical shifts [61][62][63] . The C(1s), O(1s) and N(1s) split peak spectra of 1/3 coking coal are shown in Fig. 2a-c. The proportion of the structure is calculated by the relative area, and the structure parameters of each peak position shown in Table 3.  www.nature.com/scientificreports/ contains three naphthalene, one phenanthrene, one chrysene, and one pyridinic nitrogen, the number of oxygen atoms is 30, including 24 oxygen-containing functional groups, of which 10 carbonyl oxygens, 6 carboxyl oxygens, and 8 ether bond oxygens.
The calculated X BP value is 0.296, and the final molecular formula is determined to be C 181 H 179 NO 30 . Using ChemDraw software, the analyzed molecular structure is combined and constructed, and the macromolecular structure of coking coal is shown in Fig. 3.
The molecular model was geometrically optimized and annealed in the Forcite module of Materials Studio software, and the temperature was set at 293.15 K. Based on the optimized coal molecules, a unit cell containing 7 coal molecules is established. After geometric optimization and annealing, the model with the lowest energy is selected, as shown in Fig. 4. The lattice parameters are a = b = c = 30.7748 Å and α = β = γ = 90°.

Pore characteristics of the unit cell model
For the established lowest energy unit cell model, the same stress is applied to all six faces of the unit cell. The stress is 0 GPa, 0.2 GPa, 0.4 GPa, 0.6 GPa, 0.8 GPa, 1 GPa, 1.2 GPa and 1.4 GPa, a total of 8 conditions. Then the molecular models were geometrically optimized, annealed and dynamically balanced, and the respective unit cell models were finally determined.
The density of the unit cell model under 8 kinds of stress is shown in Fig. 5. As the stress increases, the density of the unit cell gradually increases, and the rate of increase gradually decreases.
The RDF of the unit cell model under 8 kinds of stress is shown in Fig. 6. Under different stresses, the RDF of the unit cell is basically the same, indicating that the order of the unit cell is basically unchanged. www.nature.com/scientificreports/ Use the zeo + + -0.3 code to calculate the pore size, PSD, constrained stochastic ray tracing, surface area and pore volume of the unit cell under 8 kinds of stress. In order to find out the characteristics of the pores, the Monte Carlo algorithm is used, the radius of the probe is 0.5 Å, and the sample is 100,000.
Pore size. The pore size of the unit cell model under 8 kinds of stress is shown in Fig. 7. The three pore sizes are: global cavity diameter > largest cavity diameter > pore limiting diameter. As the stress increases, the global cavity diameter, pore limiting diameter, and largest cavity diameter all show a smaller decreasing trend.
The three-dimensional and cumulative PSD of the unit cell model under eight kinds of stress are shown in Fig. 8a,b. The unit cell model under 8 kinds of stress shows a large peak when the pore diameter is smaller, and a small peak when the pore diameter is larger, which indicates that the proportion of smaller pores is larger than that of larger pores. As the stress increases, the maximum pore size of the unit cell model decreases, and the range of PSD decreases, showing a trend of increasing the proportion of smaller pores and decreasing the proportion of larger pores, and the trend is gradually decreasing.
The PSD and constrained stochastic ray tracing have distinct but complementary characteristics when detecting pores 65 . The constrained stochastic ray tracing distribution of the unit cell model under 8 kinds of stress is shown in Fig. 9. The constraint stochastic ray tracing distributions of the unit cell models under the eight stress conditions are all asymmetric single peaks. The right side of the peak is much smoother than the left side, and the ray lengths corresponding to the peaks are basically the same. After being greater than the peak ray length,  www.nature.com/scientificreports/ as the ray length increases, the number of the same ray length decreases. As the stress increases, the number of rays with the same length decreases, and the speed at which the number of rays decreases gradually decreases; the number of rays with a smaller length is basically unchanged. This shows that as the stress increases, the number of all pores in the unit cell model decreases, and the rate of decrease gradually decreases, and the smaller pores are less affected.
Surface area and volume. The accessible surface area is more suitable for characterizing adsorbed porous solids than the Connolly surface area 66 . The accessible surface area depends on the size of the probe molecule.
The accessible surface area of the unit cell model under 8 kinds of stress is shown in Fig. 10. As the stress increases, the accessible surface area gradually decreases, and the rate of decrease gradually decreases. The accessible and probe-occupiable pore volume is the closest to the experimentally measured pore volume. The geometric pore volume is the upper limit of this value, while the accessible pore volume greatly underestimates the experimental value 67 .
The pore volume and volume fraction of the unit cell model under 8 kinds of stress are shown in Fig. 11a,b. The relationship between the three pore volumes is consistent with the theory. As the stress increases, the values of accessible and probe-occupiable pore volume, geometric pore volume and accessible pore volume generally  www.nature.com/scientificreports/ show a decreasing trend. The volume fraction of accessible and probe-occupiable pore volume is approximately 20%. The volume fraction of geometric pore volume is about 40%, which is twice of the volume fraction of accessible and probe-occupiable pore volume. The volume fraction of accessible pore volume is about 10%, which is half of the volume fraction of accessible and probe-occupiable pore volume.
, k = 0.48 + 1.574ω − 0.176ω 2 , T r = T/T c , ω is the acentric factor of methane, 0.008, T r is the contrast temperature , K, T is the temperature, 293.15 K, T c is the critical temperature of methane, The corresponding relationship between pressure and fugacity calculated by Eqs. (2), (3) and (4) is shown in Fig. 12. The fugacity coefficient of methane is less than 1, and decreases with the increase of pressure, and finally stabilizes.
The unit adsorption capacity of methane is equal to the ratio of the number of adsorbed methane to the molar mass of unit cell, that is, Eq. (5).
where N CH4 is the number of adsorbed methane, N M is the number of coal molecules, 7, M M is the molar mass of coal molecules, 2.845 kg/mol, x is the amount of adsorbed methane, mol/kg.

Methane adsorption results.
The simulation was carried out using the "Sorption in the Forcite" module of the Materials Studio. In the simulation, the injected pressure of methane is 0.   www.nature.com/scientificreports/ ferent stresses, the adsorption results of unit cells when the methane injection pressure is 45 MPa are shown in Fig. 13a-h. The methane injected pressure is converted to the corresponding fugacity application according to Fig. 12, and the amount of methane adsorbed by the simulation is converted according to Eq. (4). The adsorption capacity of the unit cell under the action of 8 kinds of stress under different methane injected pressure conditions is shown in Fig. 14a,b.   www.nature.com/scientificreports/ different stresses and the same methane injection pressure, the amount of methane adsorption decreases as the stress increases. The higher the methane injection pressure, the faster the amount of methane adsorption decreases with the increase of stress. Take stress as the abscissa and Langmuir adsorption constants a and b as the ordinate respectively to draw curves, as shown in Fig. 15.
With the increase of stress, the value of the limit adsorption capacity a of methane decreases, and the value of the adsorption constant b first decreases rapidly and then increases.
Overall system energies and RDF of methane. The overall system energies of the unit cell under 8 kinds of stresses under different methane injection pressure conditions is shown in Fig. 16. Langmuir fitting was performed on the overall system energies under eight kinds of stress conditions. The correlation coefficients of Langmuir fitting under the eight kinds of stress were all greater than 0.92, indicating that the overall system energies conformed to the Langmuir curve. As the stress increases, the overall system energies decrease, and as the injection pressure increases, the overall system energies increase, and the change of the overall system energies is basically the same as the change in the amount of methane adsorption.
Select the unit cell model at 45 MPa methane injection pressure under 8 kinds of stresses to calculate the RDF of methane, as shown in Fig. 17. There are two peaks in the RDF of methane, the closer peak is higher. As www.nature.com/scientificreports/ the stress increases, the peak value also increases, indicating that the greater the stress, the greater the order of the adsorbed methane. The greater the stress, the smaller the amount of methane adsorbed, and its order will increase, which is consistent with the RDF of methane.

Conclusions
The application of stress causes the pores of the unit cell to shrink, and the larger pores are reduced by a higher rate, which leads to a decrease in the methane adsorption capacity of the unit cell. The change in applied stress and the pore shrinkage of the unit cell are not linear.
1. The unit cell models under 8 kinds of stresses of 0 GPa, 0.2 GPa, 0.4 GPa, 0.6 GPa, 0.8 GPa, 1 GPa, 1.2 GPa, and 1.4 GPa were established. As the stress increases, the density of the unit cell gradually increases, and the rate of increase decreases, and the order of the unit cell remains unchanged. 2. With the increase of stress, the global cavity diameter, pore limiting diameter, and largest cavity diameter all decrease, the proportion of smaller pores increases, the proportion of larger pores decreases, and the number of pores decreases, the speed of reduction gradually decreases, and the smaller pores are less affected. As the stress increases, the accessible surface area, accessible and probe-occupiable pore volume, geometric pore volume and accessible pore volume all show a decreasing trend. 3. The fugacity coefficient of methane is less than 1, and decreases with the increase of pressure, and finally stabilizes. Under 8 kinds of stresses, the amount of methane adsorption conforms to the Langmuir adsorption curve. As the stress increases, the methane adsorption performance of the unit cell decreases, and the rate of decrease gradually decreases. The change of overall system energies is basically the same as the change of  www.nature.com/scientificreports/ amount of methane adsorption. As the stress increases, the amount of methane adsorbed decreases, and the order of methane increases.

Data availability
The primary data used to support the findings of this study are available from the corresponding author upon request.