Transport in Porous Media

, Volume 116, Issue 2, pp 493–519 | Cite as

Multi-scale Analysis of Gas Transport Mechanisms in Kerogen

  • Rui Kou
  • Saad F. K. Alafnan
  • I. Yucel AkkutluEmail author


Quantification of natural gas transport in organic-rich shale is important in predicting natural gas production. However, laboratory measurements are challenging due to tight nature of the rock and include large uncertainties. The emphasis of this work is to understand mass transport mechanisms inside the organic nanoporous material known as kerogen under subsurface conditions and describe its permeability. This requires a multi-scale theoretical approach that includes flow measurements in model nanocapillaries and within their network. Molecular dynamics simulation results of steady-state supercritical methane flow in single-wall carbon nanotube are presented in this article. A transition from convection to molecular diffusion is observed. The simulation results show that the adsorbed methane molecules are mobile and contribute a significant portion to the total mass flux in nanocapillaries with diameter \({<}\)10 nm. They experience cluster diffusion that is dependent on the applied pressure drop across the capillary. A modified Hagen–Poiseuille equation is proposed considering the convective–diffusive nature of the overall transport in nanocapillary. The molecular-level study of steady-state transport is extended to a simple network of interconnected nanocapillaries representing kerogen. The modified Hagen–Poiseuille equation leads to a representative elementary volume of the model kerogen. The estimated permeability of the volume is sensitive to compressed and adsorbed fluids density ratio and to surface properties of the nanocapillary walls, indicating that fluid–wall interactions driven by molecular forces could be significant during the large-scale transport within shale. A modified Kozeny–Carman correlation is proposed, relating kerogen porosity and tortuosity to the permeability.


Kerogen Shale permeability Shale gas transport Nanocapillary Hagen–Poiseuille Knudsen diffusion Cluster diffusion 

List of Symbols

\(A_{\text {ads}} \)

Cross section area for adsorbed-phase transport, m\(^{2}\)

\(A_{\text {diff}} \)

Cross section area for diffusion transport, m\(^{2}\)


Molar density, or concentration, mol/m\(^{3}\)


Adsorbed-phase mobility, nm\(^{2}\)/(psi  ps)


Diffusion coefficient, m\(^{2}\)/s

\(J_{\text {vis}}\)

Mass flux of viscous flow, kg/m\(^{2}\)/s

\(J_{\text {total}}\)

Total mass flux, kg/m\(^{2}\)/s

\(J_{\text {diff}}\)

Mass flux by diffusion, kg/m\(^{2}\)/s


Intrinsic permeability, m\(^{2}\)

\(k_\text {a}\)

Apparent permeability, m\(^{2}\)

\(k_{\text {app}}\)

Apparent pore network permeability, m\(^{2}\)


Knudsen number, dimensionless

\(M_{\text {CH4}}\)

Molecular weight of methane, kg/mol

\(m_{\text {total}}\)

Total mass transfer rate, kg/s

\(m_{\text {ads}}\)

Cluster diffusion mass transfer rate, kg/s

\(m_{\text {diff}}\)

Pore diffusion mass transfer rate, kg/s

\(m_{\text {vis}}\)

Viscous flow mass transfer rate, kg/s

\(m_{\text {HP}}\)

Mass transfer rate based on HP equation, kg/s

\(N_{\text {Pe}}\)

Péclet number, dimensionless

\(N_{\text {Bi}}\)

Biot number, dimensionless


Pressure, psi

\(Q_{\text {ads}}\)

Volume transfer rate of adsorbed phase, m\(^{3}\)/s

\(Q_{\text {vis}}\)

Volume transfer rate of viscous flow, m\(^{3}\)/s

\(r_{\text {tube}}\)

Radius of capillary, m

\(r_{\text {ads}}\)

Radius of capillary excluding adsorbed layer, m

\(r_{\text {avg}}\)

Average radius of capillary network, m

\(R_{\text {mf}}\)

Mass flux ratio, dimensionless


Time, femtosecond

\(V_{\text {ads}}\)

Adsorbed-phase velocity, nm/ps


Distance in x-direction, nm


Network coordination number, dimensionless

Greek Letters

\(\rho _s\)

Adsorbed-phase density, kg/m\(^{3}\)

\(\rho \)

Bulk phase density, kg/m\(^{3}\)

\(\mu \)

Viscosity, Pa\(\cdot \)s



RK has been funded by the Crisman Institute for Petroleum Engineering Research at Texas A&M University; SFKA has been funded by the King Fahad University of Petroleum and Minerals and by the Saudi Arabian Cultural Mission. The authors gratefully acknowledge their supports. RK and IYA acknowledge fruitful discussions with Dr. Khoa Bui and Sansarng Riewchotisakul on the MD flow simulations. The simulations have been performed using EOS cluster of the Supercomputing Facilities at Texas A&M University.


  1. Ambrose, R.J., Hartman, R.C., Diaz-Campos, M., Akkutlu, I.Y., Sondergeld, C.H.: Shale gas in-place calculations part I - new pore-scale considerations. SPE J. 17(1), 219–229 (2012)CrossRefGoogle Scholar
  2. Arya, G., Chang, H., Maginn, E.: Knudsen diffusivity of a hard sphere in a rough slit pore. Phys. Rev. Lett. 91(2), 26102 (2003)CrossRefGoogle Scholar
  3. Blunt, M.J.: Flow in porous media–pore-network models and multiphase flow. Curr. Opin. Colloid Interface Sci. 6, 197–207 (2001). doi: 10.1016/S1359-0294(01)00084-X CrossRefGoogle Scholar
  4. Celia, M.A., Reeves, P.C., Ferrand, L.A.: Recent advances in pore scale models for multiphase flow in porous media. Rev. Geophys. 33, 1049–1057 (1995)CrossRefGoogle Scholar
  5. Cheng, H., Cooper, A.C., Pez, G.P., Kostov, M.K., Piotrowski, P., Stuart, S.J.: Molecular dynamics simulations on the effects of diameter and chirality on hydrogen adsorption in single walled carbon nanotubes. J. Phys. Chem. B 109(9), 3780–3786 (2005)CrossRefGoogle Scholar
  6. Cristancho, D.A., Akkutlu, I.Y., Criscenti, L., Wang, Y.: Gas storage in model kerogen pores with surface heterogeneities. In: SPE-180142 Presented at the SPE EUROPEC Featured at 78th EAGE Conference and Exhibition, Vienna, Austria 30 May–2 June (2016)Google Scholar
  7. Do, D.D., Wang, K.: A new model for the description of adsorption kinetics in heterogeneous activated carbon. Carbon 36(10), 1539–1554 (1998)CrossRefGoogle Scholar
  8. Dullien, F.A.L.: Porous media: fluid transport and pore structure, 2nd edn. Academic Press, San Diego (1992)Google Scholar
  9. Fathi, E., Akkutlu, I.Y.: Mass transport of adsorbed-phase in stochastic porous medium with fluctuating porosity field and nonlinear gas adsorption kinetics. J. Transp. Porous Media 91(1), 5–33 (2012)CrossRefGoogle Scholar
  10. Fathi, E., Akkutlu, I.Y.: Lattice Boltzmann method for simulation of shale gas transport in kerogen. SPE J. 18(1), 27–37 (2013)CrossRefGoogle Scholar
  11. Feng, F., Akkutlu, I.Y.: Flow of hydrocarbons in nanocapillary: a non-equilibrium molecular dynamics study. SPE-177005, Paper Presented at the SPE Asia Pacific Unconventional Resources and Exhibition held in Brisbane, Australia, November 9–11 (2015)Google Scholar
  12. Gangi, A.F.: Variation of whole and fractured porous rock permeability with confining pressure. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 15(5), 249–257 (1978)Google Scholar
  13. Joekar-Niasar, V., Hassanizadeh, S.M.: Analysis of fundamentals of two-phase flow in porous media using dynamic pore-network models: a review [electronic resource]. Crit. Rev. Environ. Sci. Technol. 42(18), 1895–1976 (2012)Google Scholar
  14. Jorgensen, W.L., Tirado-Rives, J.: The OPLS potential function for proteins. Energy minimizations for crystals of cyclic peptides and crambin. J. Am. Chem. Soc. 110(6), 1657–1666 (1988)CrossRefGoogle Scholar
  15. Jorgensen, W.L., Maxwell, D.S., Tirado-Rives, J.: Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc. 118(45), 11225–11236 (1996)Google Scholar
  16. Kang, S., Fathi, E., Ambrose, R.J., Akkutlu, I.Y., Sigal, R.F.: Carbon dioxide storage capacity of organic-rich shales. SPE J. 16(4), 842–855 (2011)CrossRefGoogle Scholar
  17. Karniadakis, G.E., Beskok, A., Alluru, N.: Microflows and Nanoflows Fundamentals and Simulation, vol. 29. Springer, Berlin (2005)Google Scholar
  18. Kuila, U., Prasad, M., Kazemi, H.: Assessing knudsen flow in gas-flow models of shale reservoirs. Can. Soc. Explor. Geophys. Rec. 38(5), 22–27 (2013)Google Scholar
  19. Levdansky, V.V., Smolik, J., Moravec, P.: Influence of surface phenomena on free-molecule gas flow in fine channels. Int. Commun. Heat Mass Transf. 34(7), 796–800 (2007)CrossRefGoogle Scholar
  20. Liu, Qixin: Zhiyong, Cai: Study on the characteristics of gas molecular mean free path in nanopores by molecular dynamics simulations. Int. J. Mol. Sci. 15(7), 12714–12730 (2014)CrossRefGoogle Scholar
  21. Loucks, R.G., Reed, R.M., Ruppel, S.C., Jarvie, D.M.: Morphology, genesis, and distribution of nanometer-scale pores in siliceous mudstones of the Mississippian Barnett Shale. J. Sediment. Res. 79, 848–861 (2009). doi: 10.2110/jsr.2009.092 CrossRefGoogle Scholar
  22. Mehmani, A., Prodanovic, M., Javadpour, F.: Multiscale, multiphysics network modeling of shale matrix gas flows. J. Transp. Porous Media 99(2), 377–390 (2013)CrossRefGoogle Scholar
  23. Oura, K., Lifshits, V.G., Saranin, A.A., Zotov, A.V., Katayama, M.: Surface Science: An Introduction, pp. 325–340. Springer, Berlin (2003). ISBN 3-540-00545-5Google Scholar
  24. Palciauskas, V.V., Domenico, P.A.: Micro-fracture development in compacting sediments: relation to hydrocarbon-maturation kinetics. AAPG Bull. 64(6), 927–937 (1980)Google Scholar
  25. Panczyk, T., Warzocha, T.P., Szabelski, P., Rudzinski, W.: Kinetic adsorption energy distributions of rough surfaces: a computational study. Langmuir 24(16), 8719–8725 (2008)CrossRefGoogle Scholar
  26. Rahmanian, M., Aguilera, R., Kantzas, A.: A new unified diffusion—viscous-flow model based on pore-level studies of tight gas formations. SPE J. 18(1), 38–49 (2013)CrossRefGoogle Scholar
  27. Riewchotisakul, S., Akkutlu, I.Y.: Adsorption–enhanced transport of hydrocarbons in nanometer-scale organic pores. SPE-175107, Paper Presented During the SPE Annual Technical Conference and Exhibition in Houston, Texas, September 28–30 (2015)Google Scholar
  28. Rui, K.: Supercritical methane storage and transport in single-wall carbon nanotubes. MSc Thesis, Texas A&M University (2016)Google Scholar
  29. Sakhaee-Pour, A., Bryant, S.L.: Gas permeability of shale. SPE Reserv. Eval. Eng. 15(4), 401–409 (2012)CrossRefGoogle Scholar
  30. Salles, F., Ghoufi, A., Maurin, G., Bell, R.G., Mellot-Draznieks, C., Ferey, G.: Molecular dynamics simulations of breathing MOFs: structural transformations of MIL-53 (Cr) upon thermal activation and CO2 adsorption. Angew. Chem. 120(44), 8615–8619 (2008)CrossRefGoogle Scholar
  31. Sarkisov, L., Monson, P.A.: Modeling of adsorption and desorption in pores of simple geometry using molecular dynamics. Langmuir 17(24), 7600–7604 (2001)CrossRefGoogle Scholar
  32. Skoulidas, A.I.: Molecular dynamics simulations of gas diffusion in metal-organic frameworks: argon in CuBTC. J. Am. Chem. Soc. 126(5), 1356–1357 (2004)CrossRefGoogle Scholar
  33. Thomas, J.A., McGaughey, A.J.H.: Water flow in carbon nanotubes: transition to sub-continuum transport. Phys. Rev. Lett. 102(18), 184502(4) (2009)Google Scholar
  34. Wang, F.P., Reed, R.M.: Pore networks and fluid flow in gas shales. Paper SPE 124253 Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 4–7 October (2009)Google Scholar
  35. Wasaki, A., Akkutlu, I.Y: Dynamics of fracture-matrix coupling during shale gas production: pore compressibility and molecular transport effects. SPE 170830 Society of Petroleum Engineers (2015b). doi: 10.2118/175033-MS
  36. Wasaki, A., Akkutlu, I.Y.: Permeability of organic-rich shale. SPE J. 20(6), 1384–1396 (2015a)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Rui Kou
    • 1
  • Saad F. K. Alafnan
    • 1
  • I. Yucel Akkutlu
    • 1
    Email author
  1. 1.Texas A&M UniversityCollege StationUSA

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