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Adsorption-induced permeability change of porous material: a micromechanical model and its applications

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Abstract

This study focuses on developing a micromechanical model of poroelasticity with adsorption-induced permeability change occurred in porous material. The underlying pore pressure was represented by means of virial expansion to evaluate such adsorption-induced permeability change, in which the solid–gas interactions or the effects of interactions between molecules were involved. The relation between surface strain and volumetric strain under infinitesimal deformation conditions was presented to gain an explicit formulation of pore surface area with respect to volumetric strain and porosity. After the formulation of surface stress modified by Langmuir isothermal adsorption was derived, the differential micromechanical constitutive model of porous material was obtained. By providing that the ratio of current permeability to initial one was equal to the cubic ratio of current porosity to initial porosity, the differential equations for permeability change was consequently obtained. The present simulations showed that the predictions from the model are in good agreement with the experimental results of permeability change of coal induced by adsorption of CO\(_2\) and CH\(_4\) under confined pressure conditions in the literature.

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Abbreviations

\(\sigma \) :

Volumetric stress (Pa)

\(\epsilon \) :

Volumetric strain of porous media (\(-\))

\(s_{ij}\) :

Deviatoric stress tensor (Pa)

\(e_{ij}\) :

Deviatoric strain tensor (\(-\))

p :

Pore pressure (Pa)

\(p_b\) :

Bulk pressure (Pa)

\(p_a\) :

Adsorption pressure, \(p_a=p-p_b\) (Pa)

\(\varphi \) :

Change of Lagrangian porosity (\(-\))

\(\phi \) :

Porosity in the current configuration (\(-\))

\(\phi _0\) :

Porosity in the reference configuration (\(-\))

\(\sigma _s\) :

Surface stress (N/m)

\(\sigma _{s0}\) :

Initial surface stress (N/m)

\(\varepsilon _s \) :

Surface strain (\(-\))

\(\varepsilon _0 \) :

Residual surface strain (\(-\))

\(\epsilon ^s \) :

Volumetric strain of the solid matrix (\(-\))

\(\overline{V}_b \) :

Molar volume of the bulk gas (m\(^3\)/mol)

\(F_s \) :

Solid Helmholtz free energy per unit volume (J/m\(^3\))

U :

Interface free energy per unit volume (J/m\(^3\))

\(\gamma _{sf} \) :

Surface free energy of the solid–gas (J/m\(^2\))

\(\gamma _s \) :

Surface free energy of solid (J/m\(^2\))

\(\gamma _s^0 \) :

Initial surface free energy of solid (J/m\(^2\))

\(\gamma _f \) :

Surface free energy of gas (J/m\(^2\))

\(W_{sf} \) :

Work of adhesion interacted solid–gas (J/m\(^2\))

\(\mu \) :

Molar chemical potential (J/mol)

\(N_s \) :

Number of moles of surface amount excess

A :

Actual pore area per unit volume (m\(^{-1}\))

\(A_0 \) :

Initial pore area per unit volume (m\(^{-1}\))

K :

Bulk modulus (Pa)

b :

Biot coefficient (\(-\))

N :

Biot modulus (Pa)

G :

Shear modulus (Pa)

\(\Gamma \) :

Amount of adsorption (mol/m\(^2\))

\(\Gamma ^m \) :

Maximum amount of adsorption (mol/m\(^2\))

B :

Langmuir constant (Pa\(^{1}\))

\(\theta \) :

Fraction of surface covered (\(-\))

\(\mu _s+\lambda _s \) :

Elastic constants of solid surface (N/m)

R :

Gas constant (J mol\(^{-1}\,\) K\(^{-1}\))

T :

Temperature (K)

a :

Van der Waals constant (m\(^6 \,\)Pa/mol\(^2\))

\(b_v \) :

Van der Waals constant (m\(^3\)/mol)

\(c_1,c_2,\dots ,c_n \) :

Coefficients of pore pressure equation

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Acknowledgments

The financial supports from the National Science Foundation of China (Nos. 41172116, U1261212, and 51134005) are all gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, Beijing, China

    C. J. Li & J. L. Feng

  2. School of Mechanics and Civil Engineering, China University of Mining and Technology, D11, Xueyuan Road, Haidian District, Beijing, 100083, China

    C. J. Li & J. L. Feng

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Correspondence to J. L. Feng.

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Li, C.J., Feng, J.L. Adsorption-induced permeability change of porous material: a micromechanical model and its applications. Arch Appl Mech 86, 465–481 (2016). https://doi.org/10.1007/s00419-015-1041-4

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  • DOI: https://doi.org/10.1007/s00419-015-1041-4

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