Effective Stress Law for the Permeability and Deformation of Four Porous Limestones

Abstract

A fundamental question in rock physics is how the coupling of confining stress and pore pressure influences geophysical properties, which is manifested by the effective stress behavior of the porous rock. We investigated the effective stress behavior of four water-saturated limestones with porosities ranging from 13% to 30%. Unlike previous experimental studies limited to the permeability, we also characterized the effective stress coefficients for pore volume change and bulk strain. The pore spaces of three of the limestones (two allochemical oolitic and one micritic) have significant fractions of macropores and micropores. In these three limestones with dual porosity the effective stress coefficients for permeability and pore volume change were observed to be consistently greater than 1, even though that for axial strain was less than 1. In a microscopically homogeneous assemblage, the effective stress coefficients for permeability, bulk volumetric strain, and pore volume change are predicted to be equal to or less than unity. Our data therefore show that these limestones cannot be modeled as microscopically homogeneous. Berryman (1992a, https://doi.org/10.1029/92JB01593) and Berryman (1992b, https://doi.org/10.1103/PhysRevA.46.3307) analyzed theoretically a rock made up of two porous constituents, and our experimental data are in agreement with inequalities he derived for effective stress coefficients of such an assemblage. For comparison, we studied the Leitha limestone that is made up predominately of macropores. Our data showed that all three effective stress coefficients in this case were less than unity, as predicted for a microscopically homogeneous assemblage.