Determining Properties of High Compliance Porosity by Use of an Effective Medium Model Based on Crack Description in Terms of Their Normal and Shear Compliance Parameters

Abstract

An effective medium model recently developed by the present authors is applied for interpretation of known experimental data on pressure dependences of elastic wave velocities in dry and saturated rocks in order to elucidate the effect of the highly compliant fraction of the porosity. Our approach allows determining essential features of the soft defects in terms of their shear and normal compliances. For the dry defects, we found that the ratio of the normal to shear compliance may be as high as 5–7, which contrasts to the range 0.8–2.2 expected for such widely used defect models as Hertz–Mindlin contacts or elliptical cracks. The high normal compliance of the real defects results in strong decrease of Poisson’s ratio of the rock down to negative values. Here, we consider the case of a dry sandstone exhibiting negative Poisson’s ratio. For saturated samples, we found that although the normal compliance of the defects becomes smaller than the shear one, the difference is only 1.2–2.5 times. From the viewpoint of the role of “global” (in the sense of Biot) and local (squirt) fluid flows, the performed examination indicates strong domination of the squirt mechanism including the cases, for which a third, unidentified dispersion mechanism was earlier supposed.