Application of differential effective medium, magnetic pore fabric analysis, and X-ray microtomography to calculate elastic properties of porous and anisotropic rock aggregates

摘要

A differential effective medium (DEM) model is used to predict elastic properties for a set of porous and anisotropic aggregates, comprised of mixtures of calcite and muscovite. The DEM takes into consideration an anisotropic background medium with triclinic or higher symmetry, in which inclusions of idealized ellipsoidal shape are added incrementally. In general, the calculated elastic properties of a solid that contains inclusions representing "dry" pores/cracks are strongly dependent on the orientation and aspect ratio of the inclusions. Aspect ratios of inclusions in the synthetic aggregates, which consist of air-filled pores, are estimated from anisotropy of magnetic susceptibility (AMS) of samples whose pore space has been impregnated with a colloidal ferrofluid. The AMS derived pore shape geometry is used as an input value for inclusions in the DEM. Modeling results are compared with laboratory determined elastic properties, measured with ultrasonic waves. Calculated shear wave velocities agree in general well with laboratory measured S wave velocities, whereas calculated P wave velocities are typically 0.5-1.1 km/s higher than measured values. Differences between calculated and measured P wave velocities are attributed mainly to incomplete and biased ferrofluid saturation of pores. Spherical pores are preferably filled during imbibition, in comparison to thin cracks, which leads to overprediction of the calculated P wave velocities. The amount of ferrofluid that fills the pore space is dependent on the ratio of calcite to muscovite and the load used for compaction during sample synthesis. The permeability decreases with increasing muscovite content and increasing compaction load. Incomplete saturation of samples with high-muscovite content is confirmed by X-ray microtomography density contrast imaging of dry and ferrofluid saturated specimens.