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

Abstract

[1] 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.Citation: Almqvist, B. S. G., D. Mainprice, C. Madonna, L. Burlini, and A. M. Hirt (2011), Application of differential effective medium, magnetic pore fabric analysis, and X-ray microtomography to calculate elastic properties of porous and anisotropic rock aggregates,

Explaining the large variability in empirical relationships between magnetic pore fabrics and pore space properties

“…In some additional studies, the frequencies can be estimated from the instrument capabilities, and range from Hz to 920 Hz (Pfleiderer and Halls, 1990, Pfleiderer and Halls, 1993, Pfleiderer and Halls, 1994, Hrouda et al, 2000, Benson et al, 2003, Jones et al, 2006, Esteban et al, 2006, Robion et al, 2014, Humbert et al, 2012. Where neither the instrument nor measurement frequency are specified (Pfleiderer and Kissel, 1994, Louis et al, 2005, Almqvist et al, 2011, or where instruments with several operating frequencies were used (Nabawy et al, 2009), anisotropy degrees are not interpretable, and derived empirical relationships not comparable to other studies.…”

“…Traditional pore characterization methods such as X-ray tomography face trade-offs between sample size and resolution, and generate large amounts of data that need to be processed (Cnudde andBoone, 2013, Landis andKeane, 2010). For applications that require characterization of the average pore fabric, MPFs provide a promising alternative in that they describe the average pore fabric as a single second-order tensor, measured on a representative sample volume, and potentially capturing pores down to 10 nm, without being affected by mineral and grain boundary properties unlike seismic anisotropy (Robion et al, 2014, Almqvist et al, 2011, Pfleiderer and Halls, 1990, Benson et al, 2003.…”

Seismic properties and anisotropy of the continental crust: Predictions based on mineral texture and rock microstructure

“…Few studies have attempted to reconcile both the effects of the texture and small-scale heterogeneities (microstructural parameters, cracks and fractures, and melt and fluids). The self-consistent approximation and differential effective medium model are two useful approaches to take into account both the intrinsic and apparent seismic anisotropy [e.g., Mainprice, 1997;Nishizawa and Yoshino, 2001;Almqvist et al, 2011;Vasin et al, 2013;Kanitpanyacharoen et al, 2015]. Cracks and fractures are fluid bearing, brine filled in the upper crust and potentially melt bearing in the middle and lower crust.…”

Elastic anisotropy modeling of Kimmeridge shale

“…The main idea is that properties of a multiphase material (effective medium) could be numerically calculated with a stepwise procedure, by incrementally adding inclusions of one phase into the host material, which is the homogeneous effective medium obtained at the previous step. Such an approach has been applied to calculate properties of mineral aggregates, including sedimentary rocks and shales [e.g., Nishizawa , ; Hornby et al ., ; Nishizawa and Kanagawa , ; Almqvist et al ., ].…”