On the effective permeability of a heterogeneous porous medium: the role of the geometric mean

Abstract

This paper uses experimental data derived from surface permeability tests conducted on a bench-scale 508 mm cuboidal sample of Indiana Limestone. These results are used in combination with computational modelling to test the hypothesis that the geometric mean is a good proxy to represent permeability when the spatial distribution of the permeability for the heterogeneous rock, with no evidence of hydraulic anisotropy or fractures, is log-normal. The predictive capabilities of the geometric mean as a measure of the effective permeability are further assessed by examining specific examples where three-dimensional flows are initiated in the heterogeneous domain and where the equivalent homogeneous problem gives rise to purely circular flows that have exact solutions. The approach is also applied to examine a hypothetical hydraulic pulse test that is conducted on a cuboidal region with sealed lateral boundaries, consisting of the experimentally measured heterogeneous distribution of permeability and an equivalent homogeneous region where the permeability corresponds to the geometric mean.

Keywords:

• permeability heterogeneity
• effective permeability
• surface permeability tests
• computational developments
• geometric mean
• hydraulic pulse tests

Acknowledgements

The work described in this paper was supported in part through the Max Planck Research Prize in the Engineering Sciences awarded by the Max Planck Gesellschaft, Berlin, Germany and in part through NSERC Discovery Grant, both awarded to A.P.S. Selvadurai and through the NSERC PGS-D scholarship awarded to P.A. Selvadurai. The authors are grateful to a referee for the detailed comments that led to improvements in the presentation of subject matter.