A DIFFERENTIAL SCHEME FOR ELASTIC PROPERTIES OF ROCKS WITH DRY OR SATURATED CRACKS

Abstract eng:
Differential Effective Medium (DEM) theory is applied to the problem of estimating physical properties of elastic media with penny-shaped cracks, filled with gas or liquid. Cracks are assumed to be randomly oriented. Assuming that the changes in certain factors depending only on Poisson’s ratio do not strongly affect the results, the equations decouple for bulk ( ) and shear ( ) moduli, and they may be integrated analytically. The validity of this assumption is then confirmed by integrating the full DEM equations numerically. These theoretical results for the elastic constants are then compared and contrasted with results predicted by Gassmann’s equations and with results of Mavko and Jizba, for granite-like examples. Gassmann’s equations do not predict the observed liquid dependence of the shear modulus at all. Mavko and Jizba predict the observed dependence of shear modulus on liquid bulk modulus for small crack porosity, but fail to predict the observed behavior at higher porosities. In contrast, the analytical approximations derived here give very satisfactory agreement in all cases for both and .

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