Equivalent porous medium for modeling of the elastic and the sonic properties of sandstones

• Equivalent porous media are defined for modeling of sonic properties of sandstones.
• The simulation is compared with laboratory measurements
• The effect of clay content is accounted.
• The stress sensitivity is also discussed.

This study is devoted to model the elastic and the sonic properties of sandstones. The main difficulty in modeling granular materials like sandstones is the effect of grain-to-grain contacts. A new concept of an equivalent porous medium (EPM), which is a porous medium of a continuous solid matrix and pore-inclusions with an equivalent porosity that is higher than the porosity of the initial medium, is proposed to avoid this difficulty. A combination of the classical Hashin–Shtrikman (HS) approach and EPM provides an efficient simulation of the elastic properties of aggregate materials like sandstones, in comparison with experimental and numerical data in literature. The porosity of EPM of clean sandstones, that is calibrated using laboratory data, is about two times greater than that of the initial medium. The effects of clay and organic contents in shaly sandstones are also taken into account by introducing a notion of an un-supporting soft-phase. Similarly to the case of clean sandstones, the volumetric fraction of the soft-phase of EPM is about two times greater than that of the initial rock. The stress sensitivity and a comparison of this model to the heuristic modified Hashin–Shtrikman model are also discussed at the end of the paper. A power law is proposed for the dependence of the volumetric fraction of the EPM's soft-phase on the effective confining pressure. The proposed concept of EPM is proved to have many practical applications for the interpretation of sonic and seismic data of reservoir rocks.