Effective stress law for the permeability of a limestone

TL;DR

This study experimentally investigates the effective stress law for limestone permeability, revealing that pore pressure significantly influences permeability and proposing a power law model supported by microstructural analysis.

Contribution

It introduces a power law for permeability variation with effective stress and a pore-shell microstructure model explaining stress effects on limestone permeability.

Findings

Permeability increases with pore pressure and decreases with confining pressure.

The permeability-effective stress coefficient exceeds one when differential pressure surpasses a few bars.

The microstructure-based model explains the experimental permeability behavior.

Abstract

The effective stress law for the permeability of a limestone is studied experimentally by performing constant head permeability tests in a triaxial cell with different conditions of confining pressure and pore pressure. Test results have shown that a pore pressure increase and a confining pressure decrease both result in an increase of the permeability, and that the effect of the pore pressure change on the variation of the permeability is more important than the effect of a change of the confining pressure. A power law is proposed for the variation of the permeability with the effective stress. The permeability effective stress coefficient increases linearly with the differential pressure and is greater than one as soon the differential pressure exceeds few bars. The test results are well reproduced using the proposed permeability-effective stress law. A conceptual pore-shell model based on a detailed observation of the microstructure of the studied limestone is proposed. This model is able to explain the experimental observations on the effect of the total stress and of the pore pressure on the permeability of the limestone. Effective stress coefficients for the stress-dependent permeability which are greater than one are obtained. It is shown that the controlling factor is the ratio of the different bulk moduli of the various constituents of the rock. This ratio is studied experimentally by performing microhardness tests.