Abstract
The bulk and shear moduli of dry rock framework are two essential parameters for fluid substitution and shear‐wave prediction in rock physics study. The modulus ratio of the bulk to the shear modulus, in general, is assumed to be constant, irrespective of porosity, by some popular empirical models such as the critical porosity model and Krief's model, but this assumption sometimes is in disagreement with experiment. Differential effective medium (DEM) theory has been applied to the problem of estimating the physical proprerties of elastic media. The ordinary differential equations for bulk and shear moduli are coupled. By assuming the difference between the polarization factors and for dry inclusions in the DEM equation exists an almost linear relationship with the modulus ratio , this paper derives an analytical solution for dry rock modulus ratio from the differential equation. The linear relationship between and is conformed by the numerical results which calculated from the analytical formulae for the three pore shapes: sphere, needle and penny cracks. The intercept a and gradient b of the linear relationship depend on the pore geometry. The validity of this assumption is then tested by integrating the full DEM equation numerically. The analytical approximation gives a good estimate of the numerical results for the case of three given pore shapes. The experimental test shows that the analytic formula can effectively predict the modulus ratio for dry rock with porosity.
Published Version
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