Magnetic Pore Fabrics: The Role of Shape and Distribution Anisotropy in Defining the Magnetic Anisotropy of Ferrofluid‐Impregnated Samples

Abstract

Pore fabrics define physical properties of a rock, such as permeability and elasticity, both of which are important to many geological, hydrological, and environmental applications. Minerals and hence pores are often preferentially aligned, leading to anisotropy of physical properties and preferred flow directions. Preferred flow paths are defined by the shape and arrangement of pores, and a characterization of this pore fabric forms the basis for prediction of fluid flow directions. Magnetic pore fabrics (MPFs), that is, magnetic anisotropy measurements on ferrofluid-impregnated samples, are a promising and fast way to characterize the pore fabric of connected pores in 3-D, while analyzing a large number of pores with sizes down to 10 nm, without the need for any a priori knowledge about fabric orientation. Empirical relationships suggest that the MPF is related to the pore shape and orientation and approximates permeability anisotropy. This study uses models including shape and distribution anisotropy to better understand and quantify MPFs, using simple pore shapes and pore assemblies measured in previous studies. The results obtained in this study show that (1) shape anisotropy reliably predicts the MPF of single pores, (2) both shape and distribution anisotropy are needed to predict MPFs of pore assemblies, and (3) the anisotropy parameters P, L, and F are affected by the intrinsic susceptibility of the ferrofluid in addition to pore geometry. These findings can help explain some of the variability in empirical relationships and are an important step toward a quantitative understanding and application of MPFs in geological and environmental studies.Plain Language Summary To produce clean drinking water, use geothermal energy, or control contamination, it is necessary to understand how fluids flow underground. They have to find their way from pore to pore. As soon as pores are elongated or flattened, fluids can move more easily and thus faster in some directions than others. It is desirable to predict such preferred flow directions, and a good description of the pore space is needed to do so. Many methods exist to characterize the pore space, and one of these is based on the directional dependence of magnetic properties of samples, whose pores have been filled with strongly magnetic fluid. The method is efficient and promising, but unfortunately, it is not well understood how the magnetic data reflects the details of the pore space. The models developed here help define and quantify the factors controlling the observable magnetic properties. This understanding will make the method more applicable and useful in geothermal, hydrological, and environmental applications.

FinIrrSDA: A 3‐D Model for Magnetic Shape and Distribution Anisotropy of Finite Irregular Arrangements of Particles With Different Sizes, Geometries, and Orientations

“…The model presented here suggests a stronger effect of distribution anisotropy for assemblages with more than~10 particles than predicted by previous models (Biedermann, 2019;Cañón-Tapia, 1996, 2001Stephenson, 1994). This is because FinIrrSDA takes into account more interactions, also with particles at larger distances.…”

“…Comparison of FinIrrSDA to the measurements by Jones et al (2006) and the model by Biedermann (2019) for (a) bedding, (b) capillary, and (c) crack‐like fabrics. Dashed lines show changes in results of the infinite models with pore spacing.…”

“…Additional tests verified that calculations are independent of whether the three axes of a particle define a right‐handed or left‐handed coordinate system. Finally, FinIrrSDA models of finite lines and planes consisting of different numbers of particles were compared to results of published models for infinite lines or planes of regularly spaced equal particles (Biedermann, 2019; Cañón‐Tapia, 1996; Stephenson, 1994) (Figure 5). Input parameters for these models were (1) the particle dimensions along their main axes and (2) the spacing between particles.…”

“…Biedermann (2019) calculated shape and distribution anisotropy models for a range of pore spacings, constrained by the sample size, pore size, and number of pores. That study assumed infinite lines or planes and considered only nearest‐neighbor interactions.…”

“…Stephenson (1994) developed a model to calculate the distribution anisotropy of equal spherical particles arranged in either infinite lines or infinite planes at constant interparticle spacing. This model has been adapted to ellipsoidal grains or pores of equal size and shape arranged in infinite lines or planes with equal spacing (Biedermann, 2019; Cañón‐Tapia, 1996, 2001). These existing models predict shape and distribution anisotropy in simplified systems with easy geometries but are not directly applicable to natural rocks.…”