Abstract
Under the background of deep coal mining and low-carbon energy transformation, it is significant to study the gas adsorption mechanism and pore size regulation of coal to ensure the safe and efficient development of coalbed methane and promote the goal of Carbon Neutrality. Based on the GCMC method, a full pore size model of 0.4–200 nm is systematically constructed, and the adsorption behavior of CH4 in coal under different pressure conditions is simulated and analyzed, revealing the influence mechanism of pore size on adsorption characteristics. The results show that the micropore region (0.4–1.8 nm) is dominated by the coupling of potential fields on both sides of the pore wall, and the adsorption phase density is close to that of liquid methane, which conforms to D-A model. The mesoporous region (3–30 nm) shows multi-layer adsorption under the action of a single pore wall, and Langmuir model has the best fitting effect. The adsorption behavior of the macroporous region (50–200 nm) is close to that of free gas, which is more in line with BET multi-layer adsorption theory. By establishing the quantitative function relationship between the adsorption parameters such as V0(d), VL(d) and Vm(d) and the pore size, a comprehensive adsorption model suitable for the full pore size range was constructed. It was found that the adsorption phase density decreased in three stages as the pore size increased (micropores decreased by 40%, mesopores decreased by 63%). The model can accurately characterize the adsorption behavior of CH4 with full pore size, and the error is less than 6%. This error verifies the reliability of the constructed comprehensive adsorption model in predicting CH4 adsorption behavior in cross-scale pores, indicating that the model can effectively integrate the multi-adsorption mechanism dominated by micropore filling, mesoporous surface adsorption and macroporous multi-layer adsorption, which provides an important theoretical basis and prediction tool for accurate evaluation of coalbed methane reserves and optimization of development schemes.
Data availability
All data generated or analysed during this study are included in this published article(and its supplementary information files).
References
Rezk, M. G. et al. Understanding gas capillary entrapment in sandstone and carbonate aquifer rocks: Impact of gas type and pore structure. Fuel 374, 132414 (2024).
Wang, Z. et al. Investigation of Permeability Stress Induced Damage Evolution of Shallow and Deep Coal Reservoirs in the Junggar Basin, China: Z. Wang et al 1–28 (Rock Mechanics and Rock Engineering, 2025).
Guo, F. et al. Adsorption, structure, and dynamics of DNA in montmorillonite and montmorillonite–humic acid: a molecular-level insight. Langmuir 41 (16), 10424–10433 (2025).
Thommes, M. et al. Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report). Pure Appl. Chem. 87 (9-10), 1051–1069 (2015).
Zeng, F. et al. Gas transport study in the confined microfractures of coal reservoirs. J. Nat. Gas Sci. Eng. 68, 102920 (2019).
Hu, Z. et al. Hydrogen storage potential of coals: Experimental characterization across different ranks. Int. J. Hydrog. Energy. 193, 152404 (2025).
Langmuir, I. The constitution and fundamental properties of solids and liquids. Part I. Solids. J. Am. Chem. Soc. 38 (11), 2221–2295 (1916).
Marbán, G. BET adsorption reaction model based on the pseudo steady-state hypothesis for describing the kinetics of adsorption in liquid phase. J. Colloid Interface Sci. 467, 170–179 (2016).
Dubinin, M. M. & Astakhov, V. A. Development of the concepts of volume filling of micropores in the adsorption of gases and vapors by microporous adsorbents-Communication 2. Div. Chem. Sci. 20 (1), 8–12 (1971). Bulletin of the Academy of Sciences of the USSRGeneral bases of the theory of adsorption of gases and vapors on zeolites.
Feng, K. et al. Multifractal characterization of methane adsorption in Coal Pores. Langmuir 41 (22), 14548–14559 (2025).
Zhang, L. M. et al. Pore structure characteristics of high-rank coal adsorption and its influence on methane adsorption capacity. Ind. Mine Autom. 50 (07), 147–155 (2024).
Charoensuppanimit, P. et al. Modeling the temperature dependence of supercritical gas adsorption on activated carbons, coals and shales. Int. J. Coal Geol. 138, 113–126 (2015).
Seyfi, M. M., Parisa, N. & Farshad, V. Kinetic studies of structure-H hydrate using a Langmuir adsorption model: Effects of methyl cyclohexane and methyl cyclopentane as large-molecule guest substances on methane hydrate. J. Mol. Liq. 343, 117213 (2021).
Gao, J. et al. The adsorption model of the adsorption process of CH4 on coal and its thermodynamic characteristics. Colloids Surf., A. 632, 127766 (2022).
Ramesh, A. et al. Supercapacitor and room temperature H, CO2 and CH4 gas storage characteristics of commercial nanoporous activated carbon. J. Phys. Chem. Solids. 152, 109969 (2021).
Zhou, S. et al. A modified BET equation to investigate supercritical methane adsorption mechanisms in shale. Mar. Pet. Geol. 105, 284–292 (2019).
Wu, J. K. et al. High-efficient boil-off gas storage using low-temperature activated carbon adsorption. Gas Sci. Eng., 205765. (2025).
Liu, H. et al. New insight into CH4 adsorption mechanism in coal based on modeling analysis of different adsorption theories. J. Environ. Chem. Eng. 12 (4), 113174 (2024).
Peng, W. et al. Study on Evaluation of the virtual saturated vapor pressure model and prediction of adsorbed gas content in deep coalbed methane. Processes 12 (9), 1837 (2024).
Hu, B. et al. New insights into the CH4 adsorption capacity of coal based on microscopic pore properties. Fuel 262, 116675 (2020).
Song, D. et al. Heterogeneous development of micropores in medium-high rank coal and its relationship with adsorption capacity. Int. J. Coal Geol. 226, 103497 (2020).
Li, Z. et al. Multi-scale pore fractal characteristics of differently ranked coal and its impact on gas adsorption. Int. J. Min. Sci. Technol. 33 (4), 389–401 (2023).
Li, Z. et al. Full-scale pore structure characterization of different rank coals and its impact on gas adsorption capacity: A theoretical model and experimental study. Energy 277, 127621 (2023).
Li, Q. et al. Investigation on the methane adsorption capacity in coals: Considerations from nanopores by multifractal analysis. Energy Fuels. 35 (8), 6633–6643 (2021).
Li, Q. et al. CH4 adsorption capacity of coalbed methane reservoirs induced by microscopic differences in pore structure. Unconv. Resour. 4, 100097 (2024).
Yang, R. et al. Effects of nanopore structure heterogeneity of coal samples on adsorption ability and porosity-permeability variation. Energy Fuels. 37 (4), 2721–2734 (2023).
Tao, Y. R., Zhang, G. H. & Xu, H. J. Grand canonical Monte Carlo (GCMC) study on adsorption performance of metal organic frameworks (MOFs) for carbon capture. Sustainable Mater. Technol. 32, e00383 (2022).
Li, S. G. et al. Molecular simulation of adsorption of gas in coal slit model under the action of liquid nitrogen. Fuel 255, 115775 (2019).
Yin, T. et al. A new constructed macromolecule-pore structure of anthracite and its related gas adsorption: A molecular simulation study. Int. J. Coal Geol. 220, 103415 (2020).
Long, H. et al. Adsorption and diffusion characteristics of CH4, CO2, and N2 in micropores and mesopores of bituminous coal: Molecular dynamics. Fuel 292, 120268 (2021).
Metropolis, N. & Ulam, S. The Monte Carlo method. J. Am. Stat. Assoc. 44 (247), 335–341 (1949).
Stefanov, S. K. On the basic concepts of the direct simulation Monte Carlo method. Phys. Fluids. 31 (6), 067104 (2019).
Heng, J. et al. Controlled sequential Monte Carlo. Annals Stat. 48 (5), 2904–2929 (2020).
Jia, J. et al. Molecular structure characterization analysis and molecular model construction of anthracite. Plos one. 17 (9), e0275108 (2022).
Sun, H., Ren, P. & Fried, J. R. The COMPASS force field: parameterization and validation for phosphazenes. Comput. Theor. Polym. Sci. 8 (1–2), 229–246 (1998).
Savin, A. V. & Mazo, M. A. The COMPASS force field: Validation for carbon nanoribbons. Phys. E: Low-dimensional Syst. Nanostruct. 118, 113937 (2020).
Lopez-Echeverry, J. S., Reif-Acherman, S. & Araujo-Lopez, E. Peng-Robinson equation of state: 40 years through cubics. Fluid. Phase. Equilibria. 447, 39–71 (2017).
Zhang, J. et al. Effects of nano-pore and macromolecule structure of coal samples on energy parameters variation during methane adsorption under different temperature and pressure. Fuel 289, 119804 (2021).
Hu, H. et al. Small-molecule gas sorption and diffusion in coal: Molecular simulation. Energy 35 (7), 2939–2944 (2010).
Balbuena, P. B. & Gubbins, K. E. The effect of pore geometry on adsorption behavior. Stud. Surf. Sci. Catal. 87, 41–50 (1994).
Chen, G. et al. Keys to linking GCMC simulations and shale gas adsorption experiments. Fuel 199, 14–21 (2017).
Brenner, M. & Subrahmanyan, M. G. A simple formula to compute the implied standard deviation. Financial Anal. J. 44 (5), 80–88 (1988).
Acknowledgements
This research was supported by the National Research and Development of China (No.2023YFC3009002), the National Natural Science Foundation of China (No.52204237), Young Talent Fund of Association for Science and Technology of Shaanxi Province (No.20240458) . The use of the Materials Studio software package, which was supported by the College of Chemistry and Chemical Engineering of Xi’an University of Science and Technology, is gratefully acknowledged.
Funding
This research was supported by the National Research and Development of China (No.2023YFC3009002), the National Natural Science Foundation of China (No.52204237), Young Talent Fund of Association for Science and Technology of Shaanxi Province (No.20240458).
Author information
Authors and Affiliations
Contributions
Y.B. and L.Y. wrote the main manuscript text and prepared Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14. All the authors reviewed the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
Bai, Y., Yang, L., Hu, B. et al. Molecular simulation of pore size effect on CH4 adsorption characteristics in anthracite. Sci Rep (2026). https://doi.org/10.1038/s41598-026-41355-z
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598-026-41355-z
