Apparent Liquid Permeability in Mixed-Wet Shale Permeable Media

Dian Fan, Amin Ettehadtavakkol, Wendong Wang

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Apparent liquid permeability (ALP) in ultra-confined permeable media is primarily governed by the pore confinement and fluid–rock interactions. A new ALP model is required to predict the interactive effect of the above two on the flow in mixed-wet, heterogeneous nanoporous media. This study derives an ALP model and integrates the compiled results from molecular dynamics (MD) simulations, scanning electron microscopy, atomic force microscopy, and mercury injection capillary pressure. The ALP model assumes viscous forces, capillary forces, and liquid slippage in tortuous, rough pore throats. Predictions of the slippage of water and octane are validated against MD data reported in the literature. In up-scaling the proposed liquid transport model to the representative-elementary-volume scale, we integrate the geological fractals of the shale rock samples including their pore size distribution, pore throat tortuosity, and pore-surface roughness. Sensitivity results for the ALP indicate that when the pore size is below 100 nm pore confinement allows oil to slip in both hydrophobic and hydrophilic pores, yet it also restricts the ALP due to the restricted intrinsic permeability. The ALP reduces to the well-established Carman–Kozeny equation for no-slip viscous flow in a bundle of capillaries, which reveals a distinguishable liquid flow behavior in shales versus conventional rocks. Compared to the Klinkenberg equation, the proposed ALP model reveals an important insight into the similarities and differences between liquid versus gas flow in shales.

Original languageEnglish
Pages (from-to)651-677
Number of pages27
JournalTransport in Porous Media
Issue number3
StatePublished - Sep 1 2020


  • Apparent liquid permeability
  • Carman–Kozeny equation
  • Confinement effect
  • Liquid slippage
  • Nanoporous media


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