## 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 = L^{2}/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 Θ_{1} (proportional to the inverse of the smallest eigenvalue): k ≤ νΘ_{1}/F, where ν is the kinematic viscosity. We also demonstrate that νΘ_{1} ≤ DT_{1}, where T_{1} 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 ≤ DT_{1}/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 language | English (US) |
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Title of host publication | Multiphase Transport in Porous Media - 1991 |

Publisher | Publ by ASME |

Pages | 73-81 |

Number of pages | 9 |

Volume | 122 |

ISBN (Print) | 0791808432 |

State | Published - Dec 1 1991 |

Externally published | Yes |

Event | Winter Annual Meeting of the American Society of Mechanical Engineers - Atlanta, GA, USA Duration: Dec 1 1991 → Dec 6 1991 |

### Other

Other | Winter Annual Meeting of the American Society of Mechanical Engineers |
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City | Atlanta, GA, USA |

Period | 12/1/91 → 12/6/91 |

## All Science Journal Classification (ASJC) codes

- Engineering(all)