Poroelastic Effects on Gas Transport Mechanisms and Influence on Apparent Permeability in Shale


Poroelasticity and gas slippage on the walls of nanopores are two major mechanisms that regulate shale permeability concurrent with hydrocarbons depletion. Nonlinear Klinkenberg plots reported in experiments indicate that gas slippage has a complex relationship with the variation of effective stress; however, a theoretical framework that explains the underlying physics is still missing. In the present contribution, a series of experiments were designed and conducted on intact Utica shale samples to study the simultaneous effects of gas slippage and poroelasticity under constant confining and constant effective stress conditions. In addition, an apparent permeability model was developed considering the effects of rock poroelasticity and a non-constant velocity gradient for gas flow at the pore wall. The model was calibrated and tested against the presented experimental results for Utica shale as well as previously published data. Results show that the concavity in Klinkenberg plots is caused by two separate parameters, each dominant within different ranges of pore pressures: second-order gas slippage and effective stress coefficient. The model demonstrates that gas slippage is inherently coupled with effective stress at low pore pressures. However, the evolution of apparent permeability with gas pressure deviates from the classical Klinkenberg theory only when the pore diameter is sufficiently small. When the effective stress coefficient is smaller than unity, the permeability evolution deviates from the linear Klinkenberg trend only at high pore pressures. In addition to the pore size, gas slippage is found to be closely correlated with the variation of gas viscosity with pressure and temperature.


Mechanical and Aerospace Engineering


Funding for this work was provided by Ohio University’s Innovation Strategies Initiative and from the Ohio Development Services Agency under grant OCDO R17-10

Keywords and Phrases

Apparent Permeability; Effective Stress Coefficient; Gas Slippage; Gas Viscosity; Klinkenberg Plot

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2022 Elsevier, All rights reserved.

Publication Date

01 May 2022