It is of great importance to correctly predict the evolutions of reservoir transport properties due to compaction and mechanical damage occurring in anisotropic stress conditions. Structural heterogeneities at different scales, common for instance in carbonate reservoirs, can strongly alter the mechanical response and significantly influence the evolution of flow properties with stress. In a previous work5, we have reported macroscopic hydro-mechanical behaviours of analogues samples of reservoir rock (sandstone and carbonate of granular microstructure), solicited hydrostatically and triaxially at low confinement. Using a directional permeability triaxial apparatus, the permeability evolutions during compression and the effects of brittle (fracture) and plastic (pore collapse) deformations at yield, were measured. For this new study, we have selected the moderately heterogeneous Estaillades carbonate, composed of both dense and microporous calcite aggregates conferring a bimodal porosity. About 30 cylindrical samples of standard dimension for geomechanical testing were plugged in a single block and characterized in terms of porosity and density profiles. Between the different samples, porosity dispersion ranges from 24% to 31%. Additionally in a given sample, density heterogeneities can also appear as bands or clusters. Those structural heterogeneities will control the transport properties but also the mechanical response; thus, due to those multi-scale heterogeneities, the initial permeabilities vary from 50mD to 175mD with an average value of ~125mD. All those samples were compressed triaxially, up to failure, through different proportional stress-paths K (defined as the constant ratio of horizontal to vertical stress rates) representative of reservoir conditions. Evolutions of directional permeabilities, bulk and pore compressibilities were measured during loading and correlated; inelastic and yield pressures were also identified on the strains curves. A strong scattering was observed on the mechanical response both in term of compressibility and failure threshold. Using an adapted effective medium theory based on a microstructural model close to the Estaillades rock and on Hertzian fracture theory, we have normalized the inelastic and yield pressures for all the stress paths. Normalization was performed according to the porosity deviation from the average value of ~28% of all the samples. This procedure reduces efficiently the scattering, revealing a linear relation between the critical pressures and the stress path parameter; it leads to a new formulation for the critical state envelope in the 'mean stress, deviatoric stress' diagram (p,q). This envelope exhibits a negative linear trend at high mean stress and a curvature at intermediate mean stress (corresponding to the highest deviatoric stress) connecting the positive brittle failure line at lower mean stress. Normalized axial and radial iso-permeabilities and compressibilities were finally mapped in the (p, q) stress diagram and correlated to the inelastic and yield envelopes. Our results clearly show that it is feasible to measure and define a yield envelope for moderately heterogeneous rock types such as carbonates by means of an adapted Effective Medium Theory, used to normalize the critical pressures with respect to a selected heterogeneity parameter, porosity deviation for instance. Furthermore, we show that, for this carbonate, in the framework of proportional stress path loading, the normalized critical pressures evolve linearly with the stress path parameter through all the deformation regimes (from K=0 to K=1). Therefore, the attractive feature of this new yield envelope formulation relies on the fact that only two different mechanical tests are needed to define entirely the yield envelope. The most common compression tests like 'Uniaxial Compression' (UCS) and 'Hydrostatic Compression', might therefore be sufficient for some rock types, to capture the whole yield response to anisotropic stress loading.

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