Pore collapse and the plastic behavior of high porosity chalks is well known but the extent to which harder, more moderate porosity carbonates are plastic is not as clear. We have experimentally determined the elastic and plastic deformation and effect of that deformation on permeability for a suite of carbonate rocks spanning the porosity range of 14% to 42%. The depositional environment of the carbonates was a shallow marine reef with some secondary porosity development.
Biaxial compression tests were carried out along various stress paths where the ratio of axial to radial effective stress change was kept constant. Yield and failure surfaces and strain hardening response were mapped as a function of porosity. Variation in permeability and compressibility as a function of porosity, lithology, and stress path were determined. The results were modeled with a critical state-cap plasticity model.
The deformation of the carbonates generally followed a critical state cap model. The yield cap and hardening function were strongly dependent on porosity. Even moderate porosity samples (15-22%) showed significant plastic strain under stress conditions attainable in many petroleum reservoirs. The compressibility of the samples in the plastic regime was a strong function of both porosity and stress path.
One aspect of the observed deformation that did not fit critical state theory was the long transition from elastic to fully plastic behavior. We found we could represent this behavior with two cap surfaces: an initial yield surface and final hardening surface.
Permeability reduction was a strong function of stress path. Permeability reduced less for a given increase in mean stress along stress paths with higher differential stress increments. Permeability reduction due to compaction was offset by permeability enhancement due to microcracking depending on stress path and differential stress.