Permeability of a porous medium: Electrical and diffusional estimators

Y. Achdou; M. Avellaneda

Permeability of a porous medium: Electrical and diffusional estimators

Y. Achdou, M. Avellaneda

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The effective hydrodynamic radius (L) of a porous medium is defined by the relation L = √8Fk_dc, where F is the formation factor and k_dc is the dc permeability. Two approximations of this fundamental length are discussed: the diffusional estimate L≈√8DT₁ (Avellaneda and Torquato) and the electrical estimate L≈Λ (Johnson et al.). A new simple proof of the universally valid upper bound L≤√8DT₁ is given. A comparison of Λ, L and the Kozeny Carman volume-to-surface ratio is made for a class of `corrugated' capillaries, in which several relevant geometric parameters are varied. Finally, we examine the merits of both estimators on microgeometries with a wide distribution of pore sizes.

Original language	English (US)
Title of host publication	Macroscopic Behavior of Heterogeneous Materials From the Microstructure
Publisher	Publ by ASME
Pages	115-122
Number of pages	8
ISBN (Print)	0791811018
State	Published - 1992
Event	Winter Annual Meeting of the American Society of Mechanical Engineers - Anaheim, CA, USA Duration: Nov 8 1992 → Nov 13 1992

Publication series

Name	American Society of Mechanical Engineers, Applied Mechanics Division, AMD
Volume	147
ISSN (Print)	0160-8835

Other

Other	Winter Annual Meeting of the American Society of Mechanical Engineers
City	Anaheim, CA, USA
Period	11/8/92 → 11/13/92

ASJC Scopus subject areas

Mechanical Engineering

Cite this

Permeability of a porous medium: Electrical and diffusional estimators. / Achdou, Y.; Avellaneda, M.
Macroscopic Behavior of Heterogeneous Materials From the Microstructure. Publ by ASME, 1992. p. 115-122 (American Society of Mechanical Engineers, Applied Mechanics Division, AMD; Vol. 147).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Achdou, Y & Avellaneda, M 1992, Permeability of a porous medium: Electrical and diffusional estimators. in Macroscopic Behavior of Heterogeneous Materials From the Microstructure. American Society of Mechanical Engineers, Applied Mechanics Division, AMD, vol. 147, Publ by ASME, pp. 115-122, Winter Annual Meeting of the American Society of Mechanical Engineers, Anaheim, CA, USA, 11/8/92.

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AB - The effective hydrodynamic radius (L) of a porous medium is defined by the relation L = √8Fkdc, where F is the formation factor and kdc is the dc permeability. Two approximations of this fundamental length are discussed: the diffusional estimate L≈√8DT1 (Avellaneda and Torquato) and the electrical estimate L≈Λ (Johnson et al.). A new simple proof of the universally valid upper bound L≤√8DT1 is given. A comparison of Λ, L and the Kozeny Carman volume-to-surface ratio is made for a class of `corrugated' capillaries, in which several relevant geometric parameters are varied. Finally, we examine the merits of both estimators on microgeometries with a wide distribution of pore sizes.

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Permeability of a porous medium: Electrical and diffusional estimators

Abstract

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