Gassmann Modeling of Acoustic Properties of Sandclay Mixtures
Abstract
The feasibility of modeling elastic properties of a fluidsaturated sandclay mixture rock is analyzed by assuming that the rock is composed of macroscopic regions of sand and clay. The elastic properties of such a composite rock are computed using two alternative schemes.The first scheme, which we call the composite Gassmann (CG) scheme, uses Gassmann equations to compute elastic moduli of the saturated sand and clay from their respective dry moduli. The effective elastic moduli of the fluidsaturated composite rock are then computed by applying one of the mixing laws commonly used to estimate elastic properties of composite materials.In the second scheme which we call the BerrymanMilton scheme, the elastic moduli of the dry composite rock matrix are computed from the moduli of dry sand and clay matrices using the same composite mixing law used in the first scheme. Next, the saturated composite rock moduli are computed using the equations of Brown and Korringa, which, together with the expressions for the coefficients derived by Berryman and Milton, provide an extension of Gassmann equations to rocks with a heterogeneous solid matrix.For both schemes, the moduli of the dry homogeneous sand and clay matrices are assumed to obey the Krief's velocityporosity relationship. As a mixing law we use the selfconsistent coherent potential approximation proposed by Berryman.The calculated dependence of compressional and shear velocities on porosity and clay content for a given set of parameters using the two schemes depends on the distribution of total porosity between the sand and clay regions. If the distribution of total porosity between sand and clay is relatively uniform, the predictions of the two schemes in the porosity range up to 0.3 are very similar to each other. For higher porosities and mediumtolarge clay content the elastic moduli predicted by CG scheme are significantly higher than those predicted by the BM scheme.This difference is explained by the fact that the BM model predicts the fully relaxed moduli, wherein the fluid can move freely between sand and clay regions. In contrast, the CG scheme predicts the noflow or unrelaxed moduli. Our analysis reveals that due to the extremely low permeability of clays, at seismic and higher frequencies the fluid has no time to move between sand and clay regions. Thus, the CG scheme is more appropriate for clayrich rocks.
 Publication:

Pure and Applied Geophysics
 Pub Date:
 2000
 DOI:
 10.1007/PL00001119
 Bibcode:
 2000PApGe.157..811G
 Keywords:

 Key Words: Wave velocities;
 porous medium;
 clay content;
 poroelasticity.