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

## Abstract

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.

## Introduction

Coal is a complex and heterogeneous polymeric material composed of aromatic, aliphatic, various functional groups and microcrystalline graphite sheet1,2,3,4. Coal has the properties of porous media, divided into micropores (< 2 nm), mesopores (2–50 nm) and macropores (> 50 nm)5,6,7. The adsorption of methane is mainly in micropores and mesopores8,9. There are many ways to calculate the pore information of a material.

The Poreblazer program can obtain information about the pore structure, but it also has some shortcomings10. For example, when the pore size is smaller than the size of the N2 molecule, the pore size distribution (PSD) of the material cannot be displayed11. The Zeo +  + program is based on Voronoi decomposition, which can better characterize the pore structure properties12,13. The radica Voronoi tessellation can effectively calculate the pore structure of systems containing atoms of different radii14. Martin et al.15 proposed the similarity coefficient based on the void space structure of the material through Voronoi hologram. Martin et al.16 proposed an algorithm for the assembling of crystalline porous polymer structure models that can be used in Zeo +  + software. PSD characterize the proportion of different pore sizes in the research object17. Brochard et al.18 concluded that the poromechanical response of a microporous medium to adsorption significantly depends on the PSD.

The radial distribution function (RDF) is the ratio of the local density in the radial to the average bulk density of the system, which can reflect the characteristics of particle aggregation and order and structure information19,20,21,22.

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, 13C-NMR and XPS tests were performed on Nanshan 1/3 coking coal. The methods refer to literature49,50,51. The results of proximate analysis and ultimate analysis are shown in Table 1.

For the peak fitting of the 13C-NMR spectrum, the structure attribution of the carbon element is judged according to the chemical shift value52,53,54,55,56,57, and the peak fitting is shown in Fig. 1. According to the relative area value of each structure, the 13C-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, XBP, as shown in Eq. (1)58.

$${X}_{BP}=\frac{{f}_{a}^{B}}{{f}_{a}^{H}+{f}_{a}^{P}+{f}_{a}^{S}}=0.326$$
(1)

The Avantage software was used to perform peak fitting of heteroatoms (C, O, N) in XPS59, ignoring the lower content of S60, and judge the structure attribution of C, O, N elements based on chemical shifts61,62,63. 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.

### Unit cell model construction

Based on the results of proximate analysis and ultimate analysis, different aromatic hydrocarbon have different XBP values and XPS analysis results64, it is concluded that the molecule 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 XBP value is 0.296, and the final molecular formula is determined to be C181H179NO30. 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.

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 pores65. 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, 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 area66. 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 value67.

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 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.

## Molecular dynamics simulation

### Fugacity

The Soave–Redlich–Kwong equation can be expressed by the Eq. (2).68

$${Z}^{3}-{Z}^{2}-\left({B}^{2}+B-A\right)Z-AB=0$$
(2)

where Z is compression factor, $$A=a\alpha \left(T\right)p/{R}^{2}{T}^{2}$$, $$\mathrm{B}=bp/RT$$, $$\mathrm{a}=0.45724{R}^{2}{T}_{c}^{2}/{p}_{c}$$, $$b=0.08664R{T}_{c}/{p}_{c}$$, $$\mathrm{\alpha }\left(T\right)={\left[1+k\left(1-{T}_{r}^{0.5}\right)\right]}^{2}$$, $$k=0.48+1.574\omega -0.176{\omega }^{2}$$, $${T}_{r}=T/{T}_{c}$$, $$\omega$$ 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, 190.56 K, p is the pressure, MPa, $${p}_{c}$$ is the critical pressure of methane, 4.5992 MPa, R is molar gas constant, 8.31 J/(mol*K).

The fugacity coefficient of methane ($$\varphi$$) is shown in Eq. (3).

$$\mathit{ln}\varphi =Z-1-\mathit{ln}\left(Z-B\right)-\frac{A}{B}\mathit{ln}\frac{Z+B}{Z}$$
(3)

The fugacity of methane ($$f$$) is shown in Eq. (4).

$$f=\varphi p$$
(4)

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).

$$x=\frac{{N}_{\mathrm{CH}4}}{{\mathrm{M}}_{M}*{\mathrm{N}}_{\mathrm{M}}}$$
(5)

where NCH4 is the number of adsorbed methane, NM is the number of coal molecules, 7, MM is the molar mass of coal molecules, 2.845 kg/mol, x is the amount of adsorbed methane, mol/kg.

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 0.1 MPa, 1 MPa, 5 MPa, 10 MPa, 15 MPa, 20 MPa, 25 MPa, 30 MPa, 35 MPa, 40 MPa, 45 MPa, a total of 11 conditions. Under the action of different 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.

Langmuir fitting was performed on the methane adsorption capacity under 8 kinds of stress, as shown in Fig. 14a. The correlation coefficients of the Langmuir fitting under 8 kinds of stress are all greater than 0.93, indicating that the methane adsorption capacity conforms to the Langmuir adsorption curve. The amount of methane adsorption showed a Langmuir curve increase with the increase of methane injection pressure. Under 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 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. 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. 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. 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 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.

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## Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Numbers 52064046 and 51804311).

## Author information

Authors

### Contributions

S.F., H.Z., and M.G. conceived and designed the study. X.H., S.F., and Q.L. were involved in the numerical simulation. H.Z., S.F., M.G., and L.H. were involved in the data analysis. S.F., H.Z., M.G., and X.H. wrote the first draft of the manuscript. All authors have reviewed and approved the final manuscript.

### Corresponding author

Correspondence to Hongqing Zhu.

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Fang, S., Zhu, H., Gao, M. et al. Evolution of pore characteristics and methane adsorption characteristics of Nanshan 1/3 coking coal under different stresses. Sci Rep 12, 3117 (2022). https://doi.org/10.1038/s41598-022-07118-2

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• DOI: https://doi.org/10.1038/s41598-022-07118-2