Abstract

We have modeled the effective elastic moduli — and hence the compression and shear wave velocities — of dry sandstones. The modeling is distinctly different in two ranges of porosity ϕ: from zero to the consolidation limit ϕcon (consolidated regime), where the rock is treated as continuous material containing pores and cracks, and from ϕcon to the critical porosity ϕc, where the rock is transitioning to a granular material (unconsolidated regime). In the consolidated regime, the modeling is micromechanics based and yields the moduli in terms of porosity, pore-shape factor, and crack density, based on the noninteraction approximation with the Mori-Tanaka correction for interactions. By necessity, it contains empirical parameters reflecting highly irregular shapes of pores and microcracks. In the unconsolidated regime, we propose empirical relations of the Mori-Tanaka type where pore-shape factors assume large values, consistent with very soft, concave pore shapes typical in this regime. Combined, the two models can be viewed as a sand diagenesis model for the entire range of porosities, from zero to ϕc. Its predictions cover the available experimental data on arenites, the most ubiquitous group of sandstones. Finally, our empirical relations for inorganic shales express bedding-normal velocities as functions of porosity and total clay content.

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