Velocity-porosity relationships: Predictive velocity model for cemented sands composed of multiple mineral phases

Computer simulations are used to calculate the elastic properties of model cemented sandstones composed of two or more mineral phases. Two idealized models are considered - a grain-overlap clay/quartz mix and a pore-lining clay/quartz mix. Unlike experimental data, the numerical data exhibit little noise yet cover a wide range of quartz/cement ratios and porosities. The results of the computations are in good agreement with experimental data for clay-bearing consolidated sandstones. The ef fective modulus of solid mineral mixtures is found to be relatively insensitive to microstructural detail. It is shown that the Hashin-Shtrikman average is a good estimate for the modulus of the solid mineral mixtures. The distribution of the cement phase is found to have little effect on the computed modulus-porosity relationships. Numerical data for dry and saturated states confirm that Gassmann's equations remain valid for porous materials composed of multiple solid constituents. As noted previously, the Krief relationship successfully describes the porosity dependence of the dry shear modulus, and a recent empirical relationship provides a good estimate for the dry-rock Poisson's ratio. From the numerical computations, a new empirical model, which requires only a knowledge of system mineralogy, is proposed for the modulus-porosity relationship of isotropic dry or fluid-saturated porous materials composed of multiple solid constituents. Comparisons with experimental data for clean and shaly sandstones and computations for more complex, three-mineral (quartz/dolomite/clay) systems show good agreement with the proposed model over a very wide range of porosities.