Cross-property relations for transport in porous media. Rigorous link between fluid permeability, conductivity and relaxation times

Salvatore Torquato, M. Avellaneda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Rigorous relations are derived which relate the fluid permeability for flow through porous media to other measurable properties of the media. One expression relates exactly the static fluid permeability k to the electrical formation factor F (inverse of the dimensionless effective conductivity) and an effective length parameter L, i.e., k = L2/8F. This length parameter involves a certain average of the eigenvalues of the Stokes operator and reflects information about electrical and momentum transport. From the exact relation for k, a rigorous upper bound follows in terms of the principal viscous relaxation time Θ1 (proportional to the inverse of the smallest eigenvalue): k ≤ νΘ1/F, where ν is the kinematic viscosity. We also demonstrate that νΘ1 ≤ DT1, where T1 is the diffusion relaxation time for the analogous scalar diffusion problem and D is the diffusion coefficient. Therefore, one also has the alternative bound k ≤ DT1/F. The latter expression relates the fluid permeability on the one hand to purely diffusional parameters on the other. Finally, we derive an exact expression that relates the dynamic permeability to another diffusion parameter, namely, the dynamic mean survival time of a Brownian particle.

Original languageEnglish (US)
Title of host publicationMultiphase Transport in Porous Media - 1991
PublisherPubl by ASME
Pages73-81
Number of pages9
Volume122
ISBN (Print)0791808432
StatePublished - Dec 1 1991
Externally publishedYes
EventWinter Annual Meeting of the American Society of Mechanical Engineers - Atlanta, GA, USA
Duration: Dec 1 1991Dec 6 1991

Other

OtherWinter Annual Meeting of the American Society of Mechanical Engineers
CityAtlanta, GA, USA
Period12/1/9112/6/91

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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  • Cite this

    Torquato, S., & Avellaneda, M. (1991). Cross-property relations for transport in porous media. Rigorous link between fluid permeability, conductivity and relaxation times. In Multiphase Transport in Porous Media - 1991 (Vol. 122, pp. 73-81). Publ by ASME.