Higher-order correction of effective permeability of heterogeneous isotropic formations of lognormal conductivity distribution

Gedeon Dagan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

99 Scopus citations

Abstract

Steady flow of an incompressible fluid takes place in a porous formation of spatially variable hydraulic conductivity K. The latter is regarded as a lognormal stationary random space function and Y=ln(K/KG), where KG is the geometric mean of K, is characterized by its variance σ2 and correlation scale I. Exact results are known for the effective conductivity Keff in one- and two-dimensional flows. In contrast, only a first-order term in a perturbation expansion in σ2 has been derived exactly for the three-dimensional flow. A conjecture has been made in the past on Keff for any σ2, but it was not yet proved exactly. This study derived the exact nonlinear correction, i.e. the term O(σ4) of Keff, which is found to be the one resulting from the conjecture, strengthening the confidence in it. It is also shown that the self-consistent approximation leads to the exact results for one-dimensional and two-dimensional flows, but underestimates the nonlinear correction of Keff for in the three-dimensional case.

Original languageEnglish
Pages (from-to)279-290
Number of pages12
JournalTransport in Porous Media
Volume12
Issue number3
DOIs
StatePublished - Sep 1993

Keywords

  • Effective permeability
  • heterogeneous media

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